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Q4.

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.
$\begin{matrix} l \\ w & 8 \\ h & 5 \\ L.A. \\ T.A. \\ V & 360 \end{matrix}$

\begin{align} l & = 9\\w &= 8\\ h&=5\\L.A.&=170\\T.A. &= 314\\V&=360\end{align}

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The width and height of a rectangle are 8 and 5 respectively. And the volume is 360.

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.

$\begin{matrix} 360 = l \times 8 \times 5 \\ 360 = l \times 40 \\ l = \frac{360}{40} \\ l = 9 unit \end{matrix}$

Now.

$\begin{matrix} L.A. = 2 (l + w) \times h \\ = 2 (9 + 8) \times 5 \\ = 2 (17) \times 5 \\ = 34 \times 5 \\ = 170 {unit}^{2} \end{matrix}$

And

$\begin{matrix} T.A. = 72 + 2 (9 \times 8) \\ = 72 + 2 (72) \\ = 72 +144 \\ = 216 {unit}^{2} \end{matrix}$

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