# Volume of Cone

## Exercise 13.7

Question 1: Find the volume of the right circular cone with

(i) radius 6 cm, height 7 cm

**Answer:** Given: r = 6 cm, h = 7 cm

Volume of cone `=1/3πr^2h`

`=1/3xx(22)/7xx6^2xx7=264` cubic cm

(ii) radius 3.5 cm, height 12 cm

**Answer:** Given: r = 3.5 cm, h = 12 cm

Volume of cone `=1/3πr^2h`

`=1/3xx(22)/7xx3.5^2xx12=154` cubic cm

Question 2: Find the capacity in litres of a conical vessel with

(i) radius 7 cm, slant height 25 cm

**Answer:** Given; `r=7` cm, `l=25` cm

Here: `h^2=l^2-r^2`

`=25^2-7^2`

`= 625 – 49 = 576`

Or, `h=24` cm

Volume of cone `=1/3πr^2h`

`=1/3xx(22)/7xx7^2xx24=1232` cubic cm = 1.232 litre

(ii) height 12 cm, slant height 13 cm

**Answer:** Given: `h=12` cm, `l=13 `cm

Here, `r^2= l^2-h^2`

`=13^2-12^2`

= 169 – 144 = 25

Or, `r=5` cm

Volume of cone `=1/3πr^2h`

`=1/3xx3.14xx5^2xx12=314` cubic cm = 0.314 litre

Question 3: The height of a cone is 15 cm. If its volume is 1570 cm^{3}, find the radius of the base. (Use π = 3.14)

**Answer:** Given: volume = 1570 cubic cm, h = 15 cm, r = ?

Volume of cone `=1/3πr^2h`

Or, `1570=1/3xx3.14xx\r^2xx15`

Or, `r^2=(1570xx3)/(3.14xx15)=100`

Or, `r=10` cm

Question 4: If the volume of a right circular cone of height 9 cm is 48 π cm^{3}, find the diameter of its base.

**Answer:** Given: volume = 48 π cubic cm, h = 9 cm, r = ?

Volume of cone `=1/3πr^2h`

Or, `48π=1/3πr^2xx9`

Or, `r^2=(48)/3=16`

Or, `r=4` cm

Question 5: A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

**Answer:** Given: r = 3.5 m, h = 12 m

Volume of cone `=1/3πr^2h`

`=1/3xx(22)/7xx3.5^2xx12=154` cubic cm = 154 kilo litre

Question 6: The volume of a right circular cone is 9856 cm^{3}. If the diameter of the base is 28 cm, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone

**Answer:** Given: volume = 9856 cubic cm, d = 28 cm so, r = 14 cm

Volume of cone `=1/3πr^2h`

Or, `9856=1/3xx(22)/7xx14^2xx\h`

Or, `h =(9856xx3xx7)/(22xx196)=48` cm

**Slant Height:**

Here: `l^2=h^2+r^2`

`=48^2+14^2=2500`

Or, `l=50` cm

Curved surface area of cone `=πr\l`

`=(22)/7xx14xx50=2200` sq cm

Question 7: A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

**Answer:** Given: h = 12 cm, r = 5 cm

Volume of cone `=1/3πr^2h`

`=1/3π\xx5^2xx12=100π` cubic cm

Question 8: If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

**Answer:** Given: h = 5 cm, r = 12 cm

Volume of cone `=1/3πr^2h`

`=1/3π\xx12^2xx5=240π` cubic cm

Ratio `=(100)/(240)` = 5 : 12

Question 9: A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

**Answer:** Given r = 5.25 m, h = 3 m

Volume of cone `=1/3πr^2h`

`=1/3xx(22)/7xx5.25^2xx3` = 50.625 cubic m