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Q33.

Expert-verified

Geometry

Found in: Page 480

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

A diagonal of a box forms a $35^{\circ}$ angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.

The volume of box is $336.1 {unit}^{3}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

A diagonal of a box forms $35^{\circ}$ angle with a diagonal of the base.

The figure provided in the question,

Step 2. Determine the height.

Use Pythagoras theorem,

$\begin{matrix} \sqrt{{(8)}^{2} + {(6)}^{2}} = d \\ d = \sqrt{64 + 36} [square] \\ d = 10 [simplify] \end{matrix}$

Now, the height of the prism is,

$\begin{matrix} \tan 35^{\circ} = \frac{h}{10} \\ h = 10 \tan 35^{\circ} [cross multiply] \end{matrix}$

Step 3. Determine the total volume.

The volume of the box is:

$\begin{matrix} v = 8 \times 6 \times 10 \tan 35^{\circ} \\ = 336.1 [simplify] \end{matrix}$

Most popular questions for Math Textbooks

V- ABCD is a regular square pyramid. Find the following numerical answers.

$L.A. =___$

Copy and complete the table below for the regular square pyramid.

$\begin{matrix} Height, h & 12 \\ Slant Height, l & 13 \\ Base edge \\ Lateral edge \end{matrix}$

V- ABCD is a regular square pyramid. Find the following numerical answers.

$A r e a o f Δ V B C =___$

Sketch the following square pyramid described. Then find its lateral area, total area, and volume.

$Base edge = 16, Slant Height = 10$

Sketch the following pyramid. Then find its lateral area.

A regular hexagonal pyramid with base edge 10 and lateral edge 13.

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