Mensuration-48

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A cone of height 24 cm has a curved surface area 550 cm2. Find its volume.

Solution: Let the radius be r cm and slant height l cm. Then

l2 = r2 + 242

=> l = √(r2 + 576)

It is given that curved surface = 550 cm2

=> Π r l = 550

=> 22/7 x r x √(r2 + 576) = 550

=> r √(r2 + 576) = 25 x 7

=> r2 (r2 + 576) = (25 x 7)2

=> r4 + 576 r2 - (625 x 49) = 0

=> r4 + 625 r2 - 49 r2 - 625 x 49 = 0

=> r2 (r2 + 625) - 49 (r2 + 625) = 0

=> (r2 + 625) (r2 - 49) = 0

=> r2 - 49 = 0

=> r = 7 (since r2 + 625 is not equal to zero)

Therefore, Volume = 1/3 x Π r2 h = 1/3 x 22/7 x 7 x 7 x 24 cm3 = 1232 cm3

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