Question

Two similar cones have volumes 12π CU. units and 96π CU. units. If the curved surface area of smaller cone is 15π sq. units, what is the curved surface area of the larger one?

Answer 1

	Smaller cone	Larger cone
Let the radius be	r	r
volume	1/3πr2h	1/3πr2h = 96π
C.S.A	πrl = 15π	?

πrl = 15 π

\(r\sqrt{(r^2+h^2)} = 15\)

Squaring on both sides

r² (r² + h² ) = 15 x 15 

= 3 x 5 x 3 x 5

= 3 x 3 x 25

r² (r² + h² ) = 3² (3² + 4² )

∴ r = 3 cm, h = 4 cm

C.S.A. = π x 3 x (\(\sqrt{3^2+4^2}\)) = 15π