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Find the volume in terms of $π$ of a conical vessel with radius 7 cm and slant height 25 cm.

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333πcm3

395πcm3

392πcm3

390πcm3

answer is D.

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Detailed Solution

Given,

r = 7 cm l = 25 cm

.
Then using the slant height formula to find the height,

l 2 = r 2 + h 2 ⇒ (25) 2 = (7) 2 + h 2 ⇒ 625 = 49 + h 2 ⇒ 625 − 49 = h 2 ⇒ 576 = h 2 ⇒ 576 = h ⇒ 24 = h

The height of the conical vessel is 24 cm.
The volume will be,

⇒ 13 π r 2 h

⇒ 13 × π × (7) 2 × 24

⇒ 392 π c m 3

Therefore, the correct option is 4.

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