Question

Find the lateral area of a cylinder with base area of 49piin^2 and a height that is twice the radius of its base.

Answer 1

First you need to find the height:
Height = 2*radius

But we know that:
Area = pi*r^2
49piin^2 = pi*r^2
r = sqrt(49pin^2 / pi*r^2in)
r = 7 in

So height is:
Height = 2 * 7 = 14 in

Second- The lateral area (L):
The lateral area (L) is: (circuference)*height

(Circunference of the base) = 2*pi*r (inches)

So:

L = (2*pi*7)*14 (in^2)
L = 87.96 in^2