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Chapter 13 Surface Areas and Volumes Ex 13.7 Solutions

Question - 1 : -
Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm
(ii) radius 3.5 cm, height 12 cm

Answer - 1 : - (i) We have, r = 6 cm and h = 7

Question - 2 : -
Find the capacity in liters of a conical vessel with radius 7 cm, slant height 25 cm height 12 cm, slant height 13 cm
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm

Answer - 2 : -


Question - 3 : - The height of a cone is 15 cm. If its volume is 1570 cm3, then find the radius of the base (use, π = 3.14)

Answer - 3 : - Let radius of the base be r cm.

Question - 4 : - If the volume of a right circular cone of height 9 cm is 48 π cm3, then find the diameter of its base.

Answer - 4 : -

Let r be the radius of the base.
Given, volume of a right circular cone = 48π cm3

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

Answer - 5 : - Given, diameter of the top of conical pit = 3.5 m

Question - 6 : -
The volume of a right circular cone is 9856 cm3. 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 - 6 : -

We have, d = 28 cm
⇒ r = 14 cm
Volume of a right circular cone = 9856 cm3

Question - 7 : - A right angled Δ 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 - 7 : -

On revolving the right angled Δ ABC about the side AB, we get a right circular cone as shown in the adjoining figure, whose radius (r) = 5 cm and height (h) = 12 cm.
∴ Volume of the solid so obtained =  πr2h
=  x π x 5 x 5 x 12 3
= π x 5 x 5 x 4 = 100π cm3
Hence, the volume of the solid so obtained is 100π cm3.


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 - 8 : -

On revolving the right Δ ABC about the side BC(= 5 cm), we get a cone as shown in the § adjoining figure.
Volume of solid so obtained

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 - 9 : -

Given, diameter (d) = 10.5 m, then
Radius (r) = = 5.25 m and height (h)= 3 m

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