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Q13.

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Algebra 2

Found in: Page 151

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

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.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $a and b$ .

So, $a b = 35$ .

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 $b and c$ .

So, $b c = 56$ .

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

Write $a b = 35$ as follows:

$\begin{matrix} a b = 35 \\ a \cdot b = 5 \cdot 7 \end{matrix}$

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

Write $b c = 56$ as follows:

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

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 $V = a b c$ .

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

$\begin{array}{l} V = a b c \\ V = (5) (7) (8) \\ V = 280 \end{array}$

Hence, the volume of the rectangular box is 280 cubic units

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