Topic 1: MathXL for School: Topic Review

Question

The area of a label for a can is

Upper A equals 2 pi rhA=2πrh.

Use your result from part a to write a formula giving the area A of a label for a can that meets the​ manufacturer's goals. Express your answer using a single variable.

Answer 1

A = 2\pi rh

Where:

is the radius of the base of the can,

is the height of the can.

To express the area using a single variable, we need to either express in terms of or in terms of , depending on the manufacturer's goals.

If the manufacturer has a goal that relates the can’s volume, surface area, or any specific condition linking the radius and height, we can substitute one variable using that condition.

For example, if the can's volume is given by:

V = \pi r^2 h

And if we are given a fixed volume , we can solve for in terms of :

h = \frac{V_0}{\pi r^2}

Substitute this into the area formula :

A = 2\pi r \left(\frac{V_0}{\pi r^2}\right)

Simplifying the expression:

A = \frac{2V_0}{r}

Thus, the area of the label can be expressed using the radius as:

A = \frac{2V_0}{r}

This gives the area of the label in terms of a single variable, , assuming the volume is fixed.