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 `= 1/3\ π r^2\h`

`= (1/3) xx (22/7) xx 6^2\ xx 7 = 264` cubic cm

(ii) radius 3.5 cm, height 12 cm

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

Volume of cone `= 1/3\ π r^2\ h`

`= (1/3) xx (22/7) xx (3.5)^2\ xx 12 = 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 `= 1/3 \π r^2\ h`

`= (1/3) xx (22/7) xx 7^2\ xx 24 = 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 `= 1/3\ π r^2\ h`

`= (1/3) xx (3.14) xx 5^2\ xx 12 = 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 `= 1/3\ π r^2\h`

Or, `1570 = (1/3) xx (3.14) xx r^2\ xx 15`

Or, `r^2 = (1570 xx 3)/(3.14 xx 15) = 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 `= 1/3\ π r^2\ h`

Or, `48 π = 1/3 \π r^2\ xx 9`

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 `= 1/3 \π r^2\ h`

`= (1/3) xx (22/7) xx (3.5)^2\ xx 12 = 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 `= 1/3\ π r^2\ h`

Or, `9856 = (1/3) xx (22/7) xx 14^2\ xx h`

Or, `h = (9856 xx 3 xx 7)/(22 xx 196) = 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 `= π rl`

`= (22/7) xx 14 xx 50 = 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 `= 1/3 \π r^2\ h`

`= (1/3) π xx 5^2\ xx 12 = 100 π` 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 `= 1/3 \π r^2\ h`

`= (1/3) π xx 12^2\ xx 5 = 240 π` 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 `= 1/3\ π r^2\h`

`= (1/3) xx (22/7) xx (5.25)^2\ xx 3`

= 50.625 cubic m

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