Radius of a cylinder

Question

a can of beans has surface area of 334cm^2. It’s height is 11cm. What is the radius of the circular top?

Answer 1

SA_cylinder = 2*pi*r^2+2*pi*r*h

334 = 2*pi*r^2 + 2*pi*r*11

334/2/pi = r^2+11*r

0 = r^2 + 11r - 167/pi

Use quadratic formula.

r = (-11±sqrt(11^2+4*167/pi))/2 = 3.63 or -14.63278

r = 3.63 cm

Answer 2

A = 334 h=11

A = 2pi(r^2) + hpi(2r) = twice area of the top plus area of the side (area of the side is h x circumference)

334 = 2pi(r^2 +11r)

r^2 +11r = 334/2pi = 167/pi

r^2 + 11r - 167/pi - 11 = 0

r = -11/2 + .5sqr(121 + 4(167)/pi) ignore the negative square root

r = 3.63 cm