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Q3.

Expert-verified

Geometry

Found in: Page 478

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Refer to rectangular solids with dimensions l, w and h. Complete the following table.
$\begin{matrix} l & 6 \\ w & 3 \\ h \\ L.A. \\ T.A. \\ V & 54 \end{matrix}$

$\begin{matrix} l & 6 \\ w & 3 \\ h & 3 \\ L.A. & 54 \\ T.A. & 90 \\ V & 54 \end{matrix}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The length and width of a rectangle are 6 and 3 respectively. And the volume is 54.

Step 2. Write the concept.

The lateral area of the rectangle is given by:

$L.A. = Perimeter \times Height$

The total area of the rectangle is given by:

$T.A. = L.A.+ 2 (Base)$

The volume of rectangle is given by:

$V = l \times w \times h$

Step 3. Determine the value.

Firstly, find the third dimension of the rectangle using the volume.

$\begin{matrix} 54 = 6 \times 3 \times h \\ 54 = 18 \times h \\ h = \frac{54}{18} \\ h = 3 unit \end{matrix}$

Now.

$\begin{matrix} L.A. = 2 (l + w) \times h \\ = 2 (6 + 3) \times 3 \\ = 2 (9) \times 3 \\ = 18 \times 3 \\ = 54 {unit}^{2} \end{matrix}$

And

$\begin{matrix} T.A. = 54 + 2 (6 \times 3) \\ = 54 + 2 (18) \\ = 54 +36 \\ = 90 {unit}^{2} \end{matrix}$

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