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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.

(i) Diameter of the base = 28 cm

therefore

Radius of the base (r) =

28 over 2 space cm space equals space 14 space cm

Let the height of the cone be h cm.
Volume = 9856 cm³

rightwards double arrow space space space space space space space space space space space space space space 1 third πr squared straight h space equals space 9856 rightwards double arrow space space space space space space space space space space space space space space space 1 third cross times 22 over 7 cross times left parenthesis 14 right parenthesis squared cross times straight h equals 9856 rightwards double arrow space space space space space space space space space space space space space straight h space equals space fraction numerator 9856 cross times 3 cross times 7 over denominator 22 cross times left parenthesis 14 right parenthesis squared end fraction rightwards double arrow space space space space space space space space space space space space space straight h space equals space 48 space cm space

Hence, the height of the cone is 48 cm.

(ii) r = 14 cm
h = 48 cm

therefore space space space space space straight l space equals space square root of straight r squared plus straight h squared end root equals square root of left parenthesis 14 right parenthesis squared plus left parenthesis 48 right parenthesis squared end root space space space space space space space space space space equals square root of 196 plus 2304 end root equals square root of 2500 space space space space space space space space space space equals space 50 space cm

Hence, the slant height of the cone is 50 cm.
(iii) r = 14 cm
I = 50 cm
∴ Curved surface area = πrl

$equals 22 over 7 cross times 14 cross times 50 equals 2200 space cm squared$

Hence, the curved surface area of the cone is 2200 cm².

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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.

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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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