Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone
Class 9 Maths Question Answers - Surface Area and Volume of a Right Circular Cone
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Q u e s t i o n : 3 9
The height of a cone is 15 cm. If its volume is 500 p
cm
3
, then find the radius of its base.
Page 2
Q u e s t i o n : 3 9
The height of a cone is 15 cm. If its volume is 500 p
cm
3
, then find the radius of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 15 cm and that the volume of the cone is
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 100
= 10
Hence the radius of the base of the given cone is
Q u e s t i o n : 4 0
If the volume of a right circular cone of height 9 cm is 48 p
cm
3
, find the diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 9 cm and that the volume of the cone is 48 p cm
3
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 16
= 4
Hence the radius of the base of the cone with given dimensions is ‘r’ = 4 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 1
If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone=
The vertical height is given as ‘h’ = 21 cm, and the slant height is given as ‘l’ = 28 cm.
To find the base radius ‘r’ we use the relation between r, l and h.
We know that in a cone
Page 3
Q u e s t i o n : 3 9
The height of a cone is 15 cm. If its volume is 500 p
cm
3
, then find the radius of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 15 cm and that the volume of the cone is
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 100
= 10
Hence the radius of the base of the given cone is
Q u e s t i o n : 4 0
If the volume of a right circular cone of height 9 cm is 48 p
cm
3
, find the diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 9 cm and that the volume of the cone is 48 p cm
3
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 16
= 4
Hence the radius of the base of the cone with given dimensions is ‘r’ = 4 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 1
If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone=
The vertical height is given as ‘h’ = 21 cm, and the slant height is given as ‘l’ = 28 cm.
To find the base radius ‘r’ we use the relation between r, l and h.
We know that in a cone
=
=
=
Therefore the base radius is, r = cm.
Substituting the values of r = cm and h = 21 cm in the formula for volume of a cone.
Volume =
p r
2
h
3
=
p ×
v
343
2
×21
3
=2401
p
Hence the volume of the given cone with the specified dimensions is
2401 p cm
3
.
Q u e s t i o n : 4 2
The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 3.5 cm and that the volume of the cone is 3.3 liters
We know that,
1 liter = 1000 cubic centimeter
Hence, the volume of the cone in cubic centimeter is .
We can now find the radius of base ‘r’ by using the formula for the volume of a cone, while using
=
=
= 900
= 30
Hence the radius of the base of the cone with given dimensions is ‘r’ = 30 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 3
If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm
2
, find its radius.
S o l u t i o n :
It is given that the curved surface area
( )
Page 4
Q u e s t i o n : 3 9
The height of a cone is 15 cm. If its volume is 500 p
cm
3
, then find the radius of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 15 cm and that the volume of the cone is
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 100
= 10
Hence the radius of the base of the given cone is
Q u e s t i o n : 4 0
If the volume of a right circular cone of height 9 cm is 48 p
cm
3
, find the diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 9 cm and that the volume of the cone is 48 p cm
3
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 16
= 4
Hence the radius of the base of the cone with given dimensions is ‘r’ = 4 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 1
If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone=
The vertical height is given as ‘h’ = 21 cm, and the slant height is given as ‘l’ = 28 cm.
To find the base radius ‘r’ we use the relation between r, l and h.
We know that in a cone
=
=
=
Therefore the base radius is, r = cm.
Substituting the values of r = cm and h = 21 cm in the formula for volume of a cone.
Volume =
p r
2
h
3
=
p ×
v
343
2
×21
3
=2401
p
Hence the volume of the given cone with the specified dimensions is
2401 p cm
3
.
Q u e s t i o n : 4 2
The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 3.5 cm and that the volume of the cone is 3.3 liters
We know that,
1 liter = 1000 cubic centimeter
Hence, the volume of the cone in cubic centimeter is .
We can now find the radius of base ‘r’ by using the formula for the volume of a cone, while using
=
=
= 900
= 30
Hence the radius of the base of the cone with given dimensions is ‘r’ = 30 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 3
If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm
2
, find its radius.
S o l u t i o n :
It is given that the curved surface area
( )
C. S. A of the cone is 286 cm
2
and that the ratio between the base radius and the slant height is 7: 13. The formula of the
curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area = prl
Since only the ratio between the base radius and the slant height is given, we shall use them by introducing a constant ‘k’
So, r = 7k
l = 13k
Substituting the values of C.S.A, base radius, slant height and using in the above equation,
Curved Surface Area, 286 =
286 = 286 k
2
1 = k
2
Hence the value of k = 1
From this we can find the value of base radius,
r = 7k
r = 7
Therefore the base radius of the cone is
Q u e s t i o n : 4 4
Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.
S o l u t i o n :
The amount of canvas required to make a cone would be equal to the curved surface area of the cone.
The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area =
It is given that the vertical height ‘h’ = 24 m and base radius ‘r’ = 7 m.
To find the slant height ‘l’ we use the following relation
Slant height, l =
=
=
=
l = 25
Hence the slant height of the given cone is 25 m.
Now, substituting the values of r = 7 m and slant height l = 25 m and using in the formula of C.S.A,
We get
Curved Surface Area =
=
22
25
= 550
Page 5
Q u e s t i o n : 3 9
The height of a cone is 15 cm. If its volume is 500 p
cm
3
, then find the radius of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 15 cm and that the volume of the cone is
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 100
= 10
Hence the radius of the base of the given cone is
Q u e s t i o n : 4 0
If the volume of a right circular cone of height 9 cm is 48 p
cm
3
, find the diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 9 cm and that the volume of the cone is 48 p cm
3
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
=
=
= 16
= 4
Hence the radius of the base of the cone with given dimensions is ‘r’ = 4 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 1
If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone=
The vertical height is given as ‘h’ = 21 cm, and the slant height is given as ‘l’ = 28 cm.
To find the base radius ‘r’ we use the relation between r, l and h.
We know that in a cone
=
=
=
Therefore the base radius is, r = cm.
Substituting the values of r = cm and h = 21 cm in the formula for volume of a cone.
Volume =
p r
2
h
3
=
p ×
v
343
2
×21
3
=2401
p
Hence the volume of the given cone with the specified dimensions is
2401 p cm
3
.
Q u e s t i o n : 4 2
The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.
S o l u t i o n :
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
It is given that the height of the cone is ‘h’ = 3.5 cm and that the volume of the cone is 3.3 liters
We know that,
1 liter = 1000 cubic centimeter
Hence, the volume of the cone in cubic centimeter is .
We can now find the radius of base ‘r’ by using the formula for the volume of a cone, while using
=
=
= 900
= 30
Hence the radius of the base of the cone with given dimensions is ‘r’ = 30 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is
Q u e s t i o n : 4 3
If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm
2
, find its radius.
S o l u t i o n :
It is given that the curved surface area
( )
C. S. A of the cone is 286 cm
2
and that the ratio between the base radius and the slant height is 7: 13. The formula of the
curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area = prl
Since only the ratio between the base radius and the slant height is given, we shall use them by introducing a constant ‘k’
So, r = 7k
l = 13k
Substituting the values of C.S.A, base radius, slant height and using in the above equation,
Curved Surface Area, 286 =
286 = 286 k
2
1 = k
2
Hence the value of k = 1
From this we can find the value of base radius,
r = 7k
r = 7
Therefore the base radius of the cone is
Q u e s t i o n : 4 4
Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.
S o l u t i o n :
The amount of canvas required to make a cone would be equal to the curved surface area of the cone.
The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area =
It is given that the vertical height ‘h’ = 24 m and base radius ‘r’ = 7 m.
To find the slant height ‘l’ we use the following relation
Slant height, l =
=
=
=
l = 25
Hence the slant height of the given cone is 25 m.
Now, substituting the values of r = 7 m and slant height l = 25 m and using in the formula of C.S.A,
We get
Curved Surface Area =
=
22
25
= 550
Therefore the Curved Surface Area of the cone is
Q u e s t i o n : 4 5
Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.
S o l u t i o n :
The area of metal sheet required to make this hollow closed cone would be equal to the total surface area of the cone.
The formula of the total surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Total Surface Area =
It is given that the vertical height ‘h’ = 24 cm and base radius ‘r’ = 7 cm.
To find the slant height ‘l’ we use the following relation
Slant height, l =
=
=
=
l = 25
Hence the slant height of the given cone is 25 cm.
Now, substituting the values of r = 7 cm and slant height l = 25 cm and using in the specified formula,
Total Surface Area =
=
22
32
= 704
Therefore the total area of the metal sheet required to make the closed hollow cone is equal to
Q u e s t i o n : 4 6
Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is 100 p
m wide.
S o l u t i o n :
The area of cloth required to make the conical pandal would be equal to the curved surface area of the cone.
The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area = prl
It is given that the vertical height ‘h’ = 100 m and base radius ‘r’ = 240 m.
To find the slant height ‘l’ we use the following relation
Slant height, l =
=
=
=
l = 260
Read More
|
44 videos|412 docs|55 tests
|
Related Exams
About this Document
|
4.64/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation.
The notes and questions for RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone have been prepared according to the Class 9 exam syllabus. Information about RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone covers topics
like and RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Example, for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone.
Introduction of RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone in English is available as part of our Mathematics (Maths) Class 9
for Class 9 & RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone in Hindi for Mathematics (Maths) Class 9 course.
Download more important topics related with notes, lectures and mock test series for Class 9
Exam by signing up for free. Class 9: Class 9 Maths Question Answers - Surface Area and Volume of a Right Circular Cone
Description
Full syllabus notes, lecture & questions for Class 9 Maths Question Answers - Surface Area and Volume of a Right Circular Cone - Class 9 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 9 | Best notes, free PDF download
Information about RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone
In this doc you can find the meaning of RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone defined & explained in the simplest way possible. Besides explaining types of
RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone theory, EduRev gives you an ample number of questions to practice RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone tests, examples and also practice Class 9
tests
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
practice quizzes
,Sample Paper
,Semester Notes
,Exam
,mock tests for examination
,Class 9 Maths Question Answers - Surface Area and Volume of a Right Circular Cone
,Viva Questions
,MCQs
,ppt
,shortcuts and tricks
,past year papers
,Free
,Objective type Questions
,video lectures
,Important questions
,Previous Year Questions with Solutions
,Class 9 Maths Question Answers - Surface Area and Volume of a Right Circular Cone
,Extra Questions
,Class 9 Maths Question Answers - Surface Area and Volume of a Right Circular Cone
,Summary
,study material
;
Additional Information about RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone for Class 9 Preparation
RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Free PDF Download
The RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone is an invaluable resource that delves deep into the core of the Class 9 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone now and kickstart your journey towards success in the Class 9 exam.
Importance of RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone
The importance of RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone cannot be overstated, especially for Class 9 aspirants.
This document holds the key to success in the Class 9 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Notes
RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Notes on EduRev are your ultimate resource for success.
RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Class 9
The "RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone on the App
Students of Class 9 can study RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Right Circular Cone is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup