Question

for the three - part question that follows, provide your answer to each part in the given workspaces. identify each part with a coordinating response. be sure to clearly label each part. part a: write an expression to represent the surface area of a cylinder with a height twice as long as its radius. part b: write an expression to represent the total cost if the materials needed to cover the outside of the cylinder cost $8 per cm². part c: show all of your work for part a and part b.

Explanation:

Step1: Recall surface - area formula for cylinder

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$. Given that $h = 2r$. Substitute $h$ into the formula:
$S=2\pi r^{2}+2\pi r(2r)=2\pi r^{2}+4\pi r^{2}=6\pi r^{2}$.

Step2: Find total cost formula

The cost per square - centimeter is $\$8$. Let $C$ be the total cost. Then $C = 8S$. Substitute $S = 6\pi r^{2}$ into the cost formula:
$C=8\times6\pi r^{2}=48\pi r^{2}$.

Answer:

Part A: The expression for the surface area of the cylinder is $6\pi r^{2}$.
Part B: The expression for the total cost is $48\pi r^{2}$.