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 cm^{2}. What is its volume?
Solution: Total surface area of the cube = 6l^{2}
∴
Thus, the volume of the cube = l^{3} = 4^{3} = 64 cm^{3 }
Question 3. The radius of a sphere doubled. What per cent of its volume is increased?
Solution: Original volume = (4/3)πr^{3}
Increased volume = (4/3)π(2r)^{3} = 32/3πr^{3}
Increase in volume = 32/3πr^{3}  4/3πr^{3} = 28/3πr^{3}
∴ 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 = 4πr^{2 }
And curved surface area of the cylinder = 2πrh = 2πr (2r) = 4πr^{2}
(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 cm^{3}) is 1/6πr^{3}
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 cm^{2}. Find its total volume.
Solution: Let ‘r’ be radius of the sphere
∴ Total S.A. = 4 π r^{2} = 154 cm^{2}
or
Now,
Question 6. If the radius of a sphere is 3r then what is its volume?
Solution:
48 videos387 docs65 tests

NCERT Textbook: Surface Area & Volumes Doc  30 pages 
1. What is the formula for finding the surface area of a cylinder? 
2. How do you calculate the volume of a cone? 
3. How can I find the surface area of a sphere? 
4. What is the formula for finding the volume of a cuboid? 
5. How do I calculate the surface area of a pyramid? 
48 videos387 docs65 tests

NCERT Textbook: Surface Area & Volumes Doc  30 pages 

Explore Courses for Class 9 exam
