Question

BAKING A rectangular cake pan has a volume of 234 cubic inches. If the length of the pan is 9 inches and the width is 13 inches, what is the height of the pan?

Short answer

The height of the rectangular cake pan is 2 inches.

Step-by-step solution

Step 1. State the formula.

The formula of volume of a rectangular prism is $V=whl$, where V is the volume, w is the width, h is the height and l is the length of the prism.

Step 2. List the given data.

A rectangular cake pan has a volume of 234 cubic inches.

It is also given that the length of the pan is 9 inches and the width is 13 inches.

Then, $l=9\mathrm{in}.$, $w=13\mathrm{in}.$

Let the height of the pan be h.

Step 3. Calculate the height.

The shape of a rectangular cake pan is that of a rectangular prism.

Put $l=9$, $w=13$and $V=234$in $V=whl$to get,

$$\begin{gathered} 234=13\times h\times 9 \\ 234=117h \\ h=\frac{234}{117} \\ h=2 \end{gathered}$$

So, $h=2$.

Step 4. Determine the unit.

Since the units of length and width are given as inches and the unit of volume is given as cubic inches, the unit of height must be inches.

So, the height of the rectangular cake pan is 2 inches.