Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone
RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone | Mathematics (Maths) Class 9 PDF Download
| 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 : 4 7
Mark the correct alternative in each of the following:
The number of surfaces of a cone has, is
a
1
b
2
c
3
d
4
S o l u t i o n :
The surfaces or faces that a cone has are :
1 Base
2 Slanted Surface
So, the number of surfaces that a cone has is 2.
Hence the correct choice is
b.
Q u e s t i o n : 4 8
The area of the curved surface of a cone of radius 2r and slant height
l
2
, is
a
prl
b
2 prl
Page 2
Q u e s t i o n : 4 7
Mark the correct alternative in each of the following:
The number of surfaces of a cone has, is
a
1
b
2
c
3
d
4
S o l u t i o n :
The surfaces or faces that a cone has are :
1 Base
2 Slanted Surface
So, the number of surfaces that a cone has is 2.
Hence the correct choice is
b.
Q u e s t i o n : 4 8
The area of the curved surface of a cone of radius 2r and slant height
l
2
, is
a
prl
b
2 prl
c
1
2
prl
d
p(r+l)r
S o l u t i o n :
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
Here the base radius is given as ‘2r’ and the slant height is given as ‘ ’
Substituting these values in the above equation we have
Curved Surface Area =
= prl
Hence the correct choice is
a.
Q u e s t i o n : 4 9
The total surface area of a cone of radius
r
2
and length 2l, is
a
2 pr (1 +r)
b
pr 1 +
r
4
c
pr (1 +r)
d
2 prl
S o l u t i o n :
The formula of the total surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Total Surface Area =
Here it is given that the base radius is ‘ ’ and that the slant height is ‘2l’.
Substituting these values in the above equation we have
Total Surface Area =
( )
Page 3
Q u e s t i o n : 4 7
Mark the correct alternative in each of the following:
The number of surfaces of a cone has, is
a
1
b
2
c
3
d
4
S o l u t i o n :
The surfaces or faces that a cone has are :
1 Base
2 Slanted Surface
So, the number of surfaces that a cone has is 2.
Hence the correct choice is
b.
Q u e s t i o n : 4 8
The area of the curved surface of a cone of radius 2r and slant height
l
2
, is
a
prl
b
2 prl
c
1
2
prl
d
p(r+l)r
S o l u t i o n :
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
Here the base radius is given as ‘2r’ and the slant height is given as ‘ ’
Substituting these values in the above equation we have
Curved Surface Area =
= prl
Hence the correct choice is
a.
Q u e s t i o n : 4 9
The total surface area of a cone of radius
r
2
and length 2l, is
a
2 pr (1 +r)
b
pr 1 +
r
4
c
pr (1 +r)
d
2 prl
S o l u t i o n :
The formula of the total surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Total Surface Area =
Here it is given that the base radius is ‘ ’ and that the slant height is ‘2l’.
Substituting these values in the above equation we have
Total Surface Area =
( )
=
Hence the correct choice is
b.
Q u e s t i o n : 5 0
A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio
a
9 : 1
b
1 : 9
c
3 : 1
d
1 : 3
S o l u t i o n :
Since the cylinder is re cast into a cone both their volumes should be equal.
So, let Volume of the cylinder = Volume of the cone
= V
It is also given that their base radii are the same.
So, let Radius of the cylinder = Radius of the cone
= r
Let the height of the cylinder and the cone be and respectively.
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
The formula of the volume of a cylinder with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cylinder =
So we have
Volume of cone
Volume of cylinder
=
1
3
p r
2
h
cone
pr
2
h
cylinder
?
V
V
=
1
3
h
c one
h
cylinder
? 1 =
1
3
h
c one
h
cylinder
Hence the correct choice is option
c.
Q u e s t i o n : 5 1
If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is
a
1
3
pr
3
b
Page 4
Q u e s t i o n : 4 7
Mark the correct alternative in each of the following:
The number of surfaces of a cone has, is
a
1
b
2
c
3
d
4
S o l u t i o n :
The surfaces or faces that a cone has are :
1 Base
2 Slanted Surface
So, the number of surfaces that a cone has is 2.
Hence the correct choice is
b.
Q u e s t i o n : 4 8
The area of the curved surface of a cone of radius 2r and slant height
l
2
, is
a
prl
b
2 prl
c
1
2
prl
d
p(r+l)r
S o l u t i o n :
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
Here the base radius is given as ‘2r’ and the slant height is given as ‘ ’
Substituting these values in the above equation we have
Curved Surface Area =
= prl
Hence the correct choice is
a.
Q u e s t i o n : 4 9
The total surface area of a cone of radius
r
2
and length 2l, is
a
2 pr (1 +r)
b
pr 1 +
r
4
c
pr (1 +r)
d
2 prl
S o l u t i o n :
The formula of the total surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Total Surface Area =
Here it is given that the base radius is ‘ ’ and that the slant height is ‘2l’.
Substituting these values in the above equation we have
Total Surface Area =
( )
=
Hence the correct choice is
b.
Q u e s t i o n : 5 0
A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio
a
9 : 1
b
1 : 9
c
3 : 1
d
1 : 3
S o l u t i o n :
Since the cylinder is re cast into a cone both their volumes should be equal.
So, let Volume of the cylinder = Volume of the cone
= V
It is also given that their base radii are the same.
So, let Radius of the cylinder = Radius of the cone
= r
Let the height of the cylinder and the cone be and respectively.
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
The formula of the volume of a cylinder with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cylinder =
So we have
Volume of cone
Volume of cylinder
=
1
3
p r
2
h
cone
pr
2
h
cylinder
?
V
V
=
1
3
h
c one
h
cylinder
? 1 =
1
3
h
c one
h
cylinder
Hence the correct choice is option
c.
Q u e s t i o n : 5 1
If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is
a
1
3
pr
3
b
2
3
pr
3
c
3 pr
3
d
9 pr
3
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 =
Here it is given that the base radius is ’3r’ and that the vertical height is ‘3r’
Substituting these values in the above equation we get
Volume of cone =
=
Hence the correct answer is option
d.
Q u e s t i o n : 5 2
If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is
a
1 : 5
b
5 : 4
c
5 : 16
d
25 : 64
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 =
Let the volume, base radius and the height of the two cones be and respectively.
It is given that the ratio between the volumes of the two cones is 1 : 4.
Since only the ratio is given, to use them in our equation we introduce a constant ‘k’.
So, = 1k
= 4k
It is also given that the ratio between the base diameters of the two cones is 4 : 5.
Hence the ratio between the base radius will also be 4 : 5.
Again, since only the ratio is given, to use them in our equation we introduce another constant ‘p’.
So, = 4p
Page 5
Q u e s t i o n : 4 7
Mark the correct alternative in each of the following:
The number of surfaces of a cone has, is
a
1
b
2
c
3
d
4
S o l u t i o n :
The surfaces or faces that a cone has are :
1 Base
2 Slanted Surface
So, the number of surfaces that a cone has is 2.
Hence the correct choice is
b.
Q u e s t i o n : 4 8
The area of the curved surface of a cone of radius 2r and slant height
l
2
, is
a
prl
b
2 prl
c
1
2
prl
d
p(r+l)r
S o l u t i o n :
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
Here the base radius is given as ‘2r’ and the slant height is given as ‘ ’
Substituting these values in the above equation we have
Curved Surface Area =
= prl
Hence the correct choice is
a.
Q u e s t i o n : 4 9
The total surface area of a cone of radius
r
2
and length 2l, is
a
2 pr (1 +r)
b
pr 1 +
r
4
c
pr (1 +r)
d
2 prl
S o l u t i o n :
The formula of the total surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Total Surface Area =
Here it is given that the base radius is ‘ ’ and that the slant height is ‘2l’.
Substituting these values in the above equation we have
Total Surface Area =
( )
=
Hence the correct choice is
b.
Q u e s t i o n : 5 0
A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio
a
9 : 1
b
1 : 9
c
3 : 1
d
1 : 3
S o l u t i o n :
Since the cylinder is re cast into a cone both their volumes should be equal.
So, let Volume of the cylinder = Volume of the cone
= V
It is also given that their base radii are the same.
So, let Radius of the cylinder = Radius of the cone
= r
Let the height of the cylinder and the cone be and respectively.
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone =
The formula of the volume of a cylinder with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cylinder =
So we have
Volume of cone
Volume of cylinder
=
1
3
p r
2
h
cone
pr
2
h
cylinder
?
V
V
=
1
3
h
c one
h
cylinder
? 1 =
1
3
h
c one
h
cylinder
Hence the correct choice is option
c.
Q u e s t i o n : 5 1
If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is
a
1
3
pr
3
b
2
3
pr
3
c
3 pr
3
d
9 pr
3
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 =
Here it is given that the base radius is ’3r’ and that the vertical height is ‘3r’
Substituting these values in the above equation we get
Volume of cone =
=
Hence the correct answer is option
d.
Q u e s t i o n : 5 2
If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is
a
1 : 5
b
5 : 4
c
5 : 16
d
25 : 64
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 =
Let the volume, base radius and the height of the two cones be and respectively.
It is given that the ratio between the volumes of the two cones is 1 : 4.
Since only the ratio is given, to use them in our equation we introduce a constant ‘k’.
So, = 1k
= 4k
It is also given that the ratio between the base diameters of the two cones is 4 : 5.
Hence the ratio between the base radius will also be 4 : 5.
Again, since only the ratio is given, to use them in our equation we introduce another constant ‘p’.
So, = 4p
= 5p
Substituting these values in the formula for volume of cone we get,
=
=
=
=
Hence the correct answer is option
d.
Q u e s t i o n : 5 3
The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former.
The ratio of their radii is
a
2 : 1
b
4 : 1
c
8 : 1
d
1 : 1
S o l u t i o n :
The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area =
Now there are two cones with base radius, slant height and Curved Surface Area
C. S. A as , , & , , respectively.
It is given that = 2( ) and also that = 2( ). Or this can also be written as
=
=
=
=
=
Hence the correct choice is option
b.
Read More
|
44 videos|412 docs|55 tests
|
Related Exams
About this Document
|
4.87/5 Rating |
|
Nov 25, 2024 Last updated |
Document Description: RD Sharma MCQs: 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 MCQs: Surface Area and Volume of a Right Circular Cone have been prepared according to the Class 9 exam syllabus. Information about RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone covers topics
like and RD Sharma MCQs: 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 MCQs: Surface Area and Volume of a Right Circular Cone.
Introduction of RD Sharma MCQs: 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 MCQs: 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: RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone | Mathematics (Maths) Class 9
Description
Full syllabus notes, lecture & questions for RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone | Mathematics (Maths) Class 9 - 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 MCQs: Surface Area and Volume of a Right Circular Cone
In this doc you can find the meaning of RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone defined & explained in the simplest way possible. Besides explaining types of
RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone theory, EduRev gives you an ample number of questions to practice RD Sharma MCQs: 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
Extra Questions
,video lectures
,Summary
,RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone | Mathematics (Maths) Class 9
,past year papers
,mock tests for examination
,Important questions
,ppt
,Free
,Previous Year Questions with Solutions
,MCQs
,RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone | Mathematics (Maths) Class 9
,Semester Notes
,study material
,Sample Paper
,Objective type Questions
,practice quizzes
,RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone | Mathematics (Maths) Class 9
,shortcuts and tricks
,Exam
,Viva Questions
;
Additional Information about RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone for Class 9 Preparation
RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone Free PDF Download
The RD Sharma MCQs: 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 MCQs: 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 MCQs: Surface Area and Volume of a Right Circular Cone
The importance of RD Sharma MCQs: 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 MCQs: Surface Area and Volume of a Right Circular Cone Notes
RD Sharma MCQs: 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 MCQs: 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 MCQs: Surface Area and Volume of a Right Circular Cone Notes on EduRev are your ultimate resource for success.
RD Sharma MCQs: Surface Area and Volume of a Right Circular Cone Class 9 Questions
The "RD Sharma MCQs: 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 MCQs: Surface Area and Volume of a Right Circular Cone on the App
Students of Class 9 can study RD Sharma MCQs: 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 MCQs: 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 MCQs: 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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup