Question

the lateral area of a cylinder is 325 pi in2 the radius is 13 in find the following Volume. surface area 

Answer 1

Volume: 2112.5π
Surface Area: 663π

First, let's find the height of the cylinder. Using the formula for lateral surface area, 2*π*r*h:

2*π*13*h = 325π
(divide π by both sides)
26h = 325
h = 12.5 in.

Next, let's solve the surface area of the cylinder using the formula π*r²*h.

π * 13² * 12.5 = π * 169 * 12.5 = 2112.5π.

Next, let's solve the surface area using the formula 2πrh + 2πr².
 
(2 * π * 13 * 12.5) + (2 * π * 13²) = 325π + 338π = 663π.