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Expert-verified Found in: Page 151 ### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903 # The area of the base of the rectangular box is 35 square units. The area of one of the faces is 56 square units. Each of the dimensions a, b, and c is an integer greater than 1. What is the volume of the rectangular box?

The volume of the rectangular box is 280 cubic units.

See the step by step solution

## Step 1 – Describe the given data.

The area of the base of the rectangular box is 35 square units.

From the figure, the length and width of the base of the rectangular box are $a\text{and}b$.

So, $ab=35$.

The area of one of the faces of the rectangular box is 56 square units.

From the figure, the length and width of one of the face of the rectangular box are $b\text{and}c$.

So, $bc=56$.

## Step 2 – Find the values of a,b, and c.

Write $ab=35$ as follows:

$\begin{array}{c}ab=35\\ a\cdot b=5\cdot 7\end{array}$

This means, $a=5,b=7.$

Write $bc=56$ as follows:

$\begin{array}{c}bc=56\\ b\cdot c=7\cdot 8\end{array}$

This means, $b=7,c=8.$

So, $a=5,b=7,c=8$.

## Step 3 – Find volume of the rectangular box.

The formula to find the volume of a rectangular box with length a, width b and the height $c$ is $V=abc$.

Substitute $a=5,b=7,c=8$ in $V=abc$:

$\begin{array}{l}V=abc\\ V=\left(5\right)\left(7\right)\left(8\right)\\ V=280\end{array}$

Hence, the volume of the rectangular box is 280 cubic units ### Want to see more solutions like these? 