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 =

∴ The length  of the required pole (diagonal) = 

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

∴   

Thus, the volume of the cube = l³ = 4³ = 64 cm³ 

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 = 

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

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

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

or        

Now,                 

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