A cylinder with base area 169π ft sq. and a height twice the radius

I would presume you would like to find the volume of the cylinder. :)

Given the base area of cylinder is 169pie ft.^2.

The base area of cylinder is a circle, which has a formula of pie × radius^2.
169pie = pie × radius^2
{Divide both sides of equation by pie}
169 = radius^2
radius^2 = 169
{Make radius the subject of equation}
radius = +- (square root)169
{Reject the negative value and retain positive value, since radius can only be positive}
radius = 13 ft.

The height of the cylinder is twice the radius, so the height will be:
Height = radius × 2
= 13 × 2
= 26 ft.

The volume of cylinder has the formula of:
Volume of cylinder = base area × height
= pie × radius^2 × height
= pie × 13^2 × 26
= 169 × 26 × pie
= 4394pie ft. cm^3

Hope this helps! :)

P.s. If your question was not to find the area of cylinder, feel free to let me know! :)