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

(ii) h = 12
l = 13 cm

r²+ h² + l²

^{$rightwards double arrow space space space space space space r squared plus left parenthesis 12 right parenthesis squared equals left parenthesis 13 right parenthesis squared rightwards double arrow space space space space space space r squared plus 144 plus 169 rightwards double arrow space space space space space space r squared equals 169 minus 144 rightwards double arrow space space space space space space r squared equals 25 rightwards double arrow space space space space space space r space equals space square root of 25 rightwards double arrow space space space space space space r space equals space 5 therefore space space space C a p a c i t y space equals space 1 third space πr squared straight h space space space space space space space space space space space space space space equals space 1 third cross times 22 over 7 cross times left parenthesis 5 right parenthesis squared cross times 12 space space space space space space space space space space space space space space equals space 2200 over 7 space cm cubed equals 2200 over 7000 space l italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic equals italic space 11 over 35 italic space l$}

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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.

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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.

897 Views