Question

fluency and skills practice
lesson 2
finding volume using unit cubes continued
7
addition:
multiplication:
volume:
8
addition:
multiplication:
volume:
9 a box has a volume of 32 cubic inches. the box is 2 inches long and 2 inches wide. what is the height of the box? how could you pack unit cubes into the box to prove your answer is correct?

Explanation:

Step1: Recall the volume formula

The volume formula for a rectangular prism is \(V = l\times w\times h\), where \(V\) is volume, \(l\) is length, \(w\) is width, and \(h\) is height.

Step2: Substitute the known values

We know that \(V = 32\) cubic inches, \(l = 2\) inches, and \(w = 2\) inches. Substitute these into the formula: \(32=2\times2\times h\).

Step3: Simplify the equation

First, calculate \(2\times2 = 4\). So the equation becomes \(32 = 4h\).

Step4: Solve for \(h\)

Divide both sides of the equation by \(4\): \(h=\frac{32}{4}\).

Step5: Calculate the value of \(h\)

\(\frac{32}{4}=8\) inches.

To prove, since each unit - cube has a volume of \(1\) cubic inch. The base of the box (area \(l\times w=2\times2 = 4\) square inches) can hold \(4\) unit - cubes. With a height of \(8\) inches, the total number of unit - cubes is \(4\times8=32\), which is equal to the volume of the box.

Answer:

The height of the box is \(8\) inches.