What will be the volume of the double cone so formed, if a right triangle whose sides are 15cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse?

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3768 cm 3

3760 cm 3

3750 cm 3

3790 cm 3

answer is A.

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Detailed Solution

Given,
A right triangle whose sides are 15cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse.
We have to find the volume of the double cone.

Pythagoras theorem, A C = A B 2 + B C 2

Calculating the hypotenuse (AC),
Question Image

A C = A B 2 + B C 2 A C = 225 + 400 A C = 25 c m

Calculating the radius of the cone,

∴ 12 × A C × B O = 12 × A B × B C ⇒ 25 × r = 15 × 20 ⇒ r = 12 cm

Calculating the volume of the double cone,

= 13 π r 2 h + 13 π r 2 H = 13 π r 2 (h + H) = 13 × 3.14 × 12 × 12 × 25 = 3768 cm 3

Volume of the double cone= 3768 cm3.
Therefore, option 1 is correct.

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