Question

The surface area S(r) in square units of a cylinder with a volume of 18 cubic units is a function of its radius

r in units where
S(r)=2πr
^2+36 / r . What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units? (Do not round your answer.)

a) 54π square units
b) 63π square units
c) 72π square units
d) 81π square units

Answer 1

The surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 18π + 12.

Step-by-step explanation:

To find the surface area of a cylinder with a given volume and radius, we can use the formula S(r) = 2πr^2 + 36/r. In this case, the volume is given as 18 cubic units and the radius is 3 units. Substituting the values into the formula, we have S(3) = 2π(3)^2 + 36/3. Simplifying this expression, we get S(3) = 18π + 12. Since the answer options are given in terms of π, we can leave the result as 18π + 12.