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Question

A clown’s cap is in the shape of a cone of height 8cm and diameter 12cm. A cut is made from the apex of the cone such that slant height of the newly formed cone is 5cm. Find the ratio of volume of the frustum of the cone formed due to the cut to the volume of the cap.


A

0.3

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B

0.325

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C

0.35

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D

0.875

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Solution

The correct option is D

0.875


Slant height of the cap = 10cm

Let r be the smaller radius of the frustum and h be height of the frustum.

ABC = ADE = 90
(right circular cone)
A = A (common angle)
Therefore ABC ~ ADE
(by AA similarity)

So, ABAD=BCDE=ACAE AB8=r6=510

So height of the frustum AB =
4010=4cm

Therefore , AB = 4cm and r = 3cm

Ratio of volume of frustum to the cap =
Volume of the frustumVolume of the cap

= 13πh(r12+r22+r1r2)13πR2H

= h(r12+r22+r1r2)R2H

= 4(36+9+18)36×8

= 4×6336×8=78=0.875


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