Question

4. The radius and height of a right circular cone
hare in the ratio si12 If its volume is 314
cubic um find the total surface area [Take π = 22/7 )

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Answer 1

Radius and height of a right circular cone are in the ratio of 5:12.

Let the radius and height be 5x, 12x respectively.

Volume of cone = 314 cm3. (given) We know, Volume of cone = 1/3 πr2h 1/3 πr2 h

= 314 1/3 x 22/7 x (5x)2 x 12x

= 314 300 x3

= 300 or x = 1

This implies,

Radius = 5 cm and Height = 7 cm

Slant height(l) = √(h2 + r2) √122 + 52 l

= √144 + 25 l

= √169 or l = 13 cm.

We know, Total surface area = πr(l + r) = 22/7 x 5 (13+5)

= 282.6 cm²

hope it helps you ☺️