Question

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)

Answer 1

Explanation:

V = 4πR³/3 + πR²h

h = (V - 4πR³/3) / πR²

A = 4πR² + 2πRh

A = 4πR² + 2πR((V - 4πR³/3) / πR²)

A = 4πR² + 2((V - 4πR³/3) / R)

A = 4πR² + 2V/ R - (8πR³/3) / R

A = 4πR² + 2(14)/ R - 8πR²/3

A = (4π - 8π/3)R² + 28/R

A = (4π/3)R² + 28/R

dA/dR = (8π/3)R - 28/R²

0 = (8π/3)R - 28/R²

28/R² = (8π/3)R

R³ = 28(3 / 8π)

R = 1.49513...

R = 1.50 cm

which makes the cylinder height 0.00 cm. The figure is a sphere.