Chapter 12: Q33. (page 480)

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.

Short Answer

Expert verified

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

Step by step solution

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,

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

Step 3. Determine the total volume.

The volume of the box is:

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

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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.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the height.

Step 3. Determine the total volume.

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A diagonal of a box forms a35∘angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the height.

Step 3. Determine the total volume.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Probability and Statistics

Applied Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

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.