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Surface Areas and Volumes

Short Answer Type

191. Find the capacity in litres of a conical vessel with
(ii) height 12 cm, slant height 13 cm.

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192. The height of a cone is 15 cm. If its volume is 1570 cm³, find the radius of the base. (Use

straight pi

= 3.14)

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193. If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.

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

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Long Answer Type

195.

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.

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Short Answer Type

196. 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.

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197. 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 Question 7 and 8.

The solid obtained will be a right circular cone whose radius of the base is 12 cm and height is 5 cm.
∴ r = 12 cm h = 5 cm

$therefore space space Volume space equals space 1 third πr squared straight h space space space space space space space space space space space space space space equals space 1 third cross times straight pi cross times left parenthesis 12 right parenthesis squared cross times 5 space cm cubed space space space space space space space space space space space space space space space equals space 240 straight pi space cm cubed$

Ratio of the volumes of the two solids obtained = 100
∴: 240
∴ = 5 : 12

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198. 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.

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