Determine the Function

Question

Determine the function described and then use it to answer the question.

The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by A = 2𝜋r² + 2𝜋rh.

 If the height of the cylinder is 4 feet, express the radius as a function of A.

r(A) = 

 

Find the radius if the surface area is 380 square feet. (Round your answer to two decimal places.)

 ft

Answer 1

A = 2pi(r^2) +2pi(r)(h)

= 2pi(r^2 +4r)

r^2+4r = A/2pi

complete the square

r^2 +4r + 4 = A/2pi + 4

take square roots of both sides

(r+2) =sqr(A/2pi + 4)

r(A)=-2 + sqr(A/2pi + 4) (ignore the negative square root to get a positive radius)