Chapter 8.3, Problem 6STP

A soup can that is a cylinder has a radius of $2x-1$ and a height of 3x. What is the surface area of the soup can? Show your work.

To determine

To find: the surface area of the soup can.

Answer to Problem 6STP

  $3\pi x{\left(2x-1\right)}^2$ square units

Explanation of Solution

Given information: A soup can is a cylinder has a radius $2x-1$ and a height of 3x.

Simplification:

Let r and h be the radius and height of the cylindrical soup can where $r=2x-1$ and $h=3x$ .

We know that area of a cylinder with radius r and h is

  $A=\pi r^{2}h$

Substitute the values of r and h .

  $\begin{array}{l}A=\pi {\left(2x-1\right)}^2\left(3x\right)\\ A=3\pi x{\left(2x-1\right)}^2\end{array}$

Thus, area of the cylindrical can is $3\pi x{\left(2x-1\right)}^2$ square units.