Important key points

Example 7.15
Find the volume of a cylinder whose height is 2 m and whose base area is 250 $m^2$.

Example 7.16
The volume of a cylindrical water tank is 1.078 × $10^6$ litres. If the diameter of the tank is 7 m, find its height.

Example 7.17
Find the volume of the iron used to make a hollow cylinder of height 9 cm and whose internal and external radii are 21 cm and 28 cm respectively.

Example 7.18
For the cylinders A and B (Fig. 7.27), (i) find out the cylinder whose volume is greater. (ii) verify whether the cylinder with greater volume has greater total surface area. (iii) find the ratios of the volumes of the cylinders A and B.

Example 7.19
The volume of a solid right circular cone is 11088 $cm^3$. If its height is 24 cm then find the radius of the cone.

Example 7.20
The ratio of the volumes of two cones is 2:3. Find the ratio of their radii if the height of second cone is double the height of the first.

Example 7.21
The volume of a solid hemisphere is 29106 $cm^3$. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

Example 7.22
Calculate the mass of a hollow brass sphere if the inner diameter is 14 cm and thickness is 1mm, and whose density is 17.3 g/$cm^3$. (Hint: mass = density × volume)

Example 7.23
If the radii of the circular ends of a frustum which is 45 cm high are 28 cm and 7 cm, find the volume of the frustum.

Important Key Points

Exercise 7.2

1. A 14 m deep well with inner diameter 10 m is dug and the earth taken out is evenly spread all around the well to form an embankment of width 5 m. Find the height of the embankment.

2. A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed completely. Calculate the raise of the water in the glass?

3. If the circumference of a conical wooden piece is 484 cm then find its volume when its height is 105 cm.

4. A conical container is fully filled with petrol. The radius is 10m and the height is 15 m. If the container can release the petrol through its bottom at the rate of 25 cu. meter per minute, in how many minutes the container will be emptied. Round off your answer to the nearest minute.

5. A right angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.

6. The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3. Find the ratio of heights.

7. If the ratio of radii of two spheres is 4:7, find the ratio of their volumes.

8. A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3$\sqrt{3}$ : 4 .

9. The outer and the inner surface areas of a spherical copper shell are 576$\pi$ $cm^2$ and 324$\pi$ $cm^2$ respectively. Find the volume of the material required to make the shell.

10. A container open at the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill a container at the rate of ₹40 per litre.