The surface area of a cylinder is 200cm. The diameter is equal to the height. Find the radius.
Cylinder SA = 2 pi r h + 2 pi r^2
diameter d = height = h
radius r = 1/2 d = 1/2 h
200 = 2 pi 1/2 * h * h + 2 pi (1/2 h)^2
200 = 2(pi)(1/2 h^2) + 2(pi)(1/4 h^2)
200 = 2/2(pi)(h^2) + 2/4(pi)(h^2)
200 = 4/4(pi)(h^2) + 2/4(pi)(h^2)
200 = 6/4(pi)(h^2)
200 = 3/2(pi)(h^2)
400 = 3 (pi)(h^2)
133.3333 = pi h^2
133.3333 = (3.14)h^2
42.46283 = h^2
h = + - 6.516351
h = 6.516351 (height cannot be neg.)
radius r = 1/2 d = 1/2 h
radius r = 1/2 6.516351 = 3.258176