Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Very Short Answer Type Questions: Surface Areas & Volumes

Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Question 1. What is the longest pole that can be put in a room of dimensions l = 10 cm, b = 10 cm and h = 5 cm?
 Solution: 
The longest diagonal of a cuboid =Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

∴ The length  of the required pole (diagonal) = Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

 

Question 2. Total surface area of a cube is 96 cm2. What is its volume?
 Solution:
Total surface area of the cube = 6l2

∴   Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Thus, the volume of the cube = l3 = 43 = 64 cm


Question 3. The radius of a sphere doubled. What per cent of its volume is increased?
 Solution:
Original volume = (4/3)πr3

Increased volume = (4/3)π(2r)3 = 32/3πr3

Increase in volume =  32/3πr3 -  4/3πr3 = 28/3πr3

∴ Per cent increase in volume = Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

 

Question 4. Write ‘True or False’ for the following statements: (i) A right circular cylinder just encloses a sphere of radius r as shown in the figure. The area of the sphere is equal to the curved surface area of the cylinder.
 Solution:
True.

∵ [Radius of the sphere] = [Radius of the cylinder] = r

Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

∴ Diameter of the sphere = 2r
⇒ Height of the cylinder (h) = 2r
Now, surface area of the sphere = 4πr
And curved surface area of the cylinder = 2πrh = 2πr (2r) = 4πr2

(ii) An edge of a cube measures ‘r’ cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in cm3) is 1/6πr3
Solution: False.
∵ Height of the cone = r cm
∴ Diameter of the base of the cone = r cm

⇒ Radius of the base of the cone = (r/2) cm

Now volume of the cone Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

 

Question 5. If the total surface area of a sphere is 154 cm2. Find its total volume.
 Solution:
Let ‘r’ be radius of the sphere
∴ Total S.A. = 4 π r2 = 154 cm2

Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

or        Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Now,                 Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

 

Question 6. If the radius of a sphere is 3r then what is its volume?
 Solution:

Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

The document Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes

1. What is the formula for finding the surface area of a cylinder?
Ans. The formula for finding the surface area of a cylinder is 2πr(r+h), where r is the radius of the base and h is the height of the cylinder.
2. How do you calculate the volume of a cone?
Ans. The formula for calculating the volume of a cone is (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
3. How can I find the surface area of a sphere?
Ans. The formula for finding the surface area of a sphere is 4πr², where r is the radius of the sphere.
4. What is the formula for finding the volume of a cuboid?
Ans. The formula for finding the volume of a cuboid is l × b × h, where l is the length, b is the breadth, and h is the height of the cuboid.
5. How do I calculate the surface area of a pyramid?
Ans. The formula for calculating the surface area of a pyramid depends on the shape of the base. For example, the surface area of a pyramid with a rectangular base is given by the formula l × w + l√((w/2)² + h²), where l is the length, w is the width, and h is the height of the pyramid.
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