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Chapter 12: Q27. (page 486)

Use trigonometry to find the volume of the regular pyramid below to the near cubic unit.

Short Answer

Expert verified

Volume=66  unit3

Step by step solution

01

Step 1. Given information.

The regular pyramid is given below.

02

Step 2. Explanation.

The formula for the volume of pyramid is the one third of the product of base area and height.

V=13Bh

Consider the tangent of the angle50° for the height of the hexagonal pyramid.

h=(base edge)×tan50°=4×tan50°=4tan50°

Simplify the base area of hexagonal triangle with side4 .

B=332a2=332(4)2=332(16)=243

03

Step 3. Determine The volume.

Substitute243 for B and4tan50° for h in the formula for volume of pyramid.

V=13Bh=13(243)(4tan50°)=323tan50°

Substitute1.191 fortan50° in the formula for volume.

V=323tan50°=32×3×1.191=66.01

Therefore, the volume of the regular pyramid to the nearest cubic unit is equal to 66.

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Most popular questions from this chapter

Show that the ratio of the volumes of the two regular square pyramids is tan40°tan80°.

A rectangular beam of wood 3 m long is cut into 6 pieces. Find the volume of each piece in cubic centimetres.

Suppose the manufacturing company cuts square corners out of pieces of metal that measure 8 inches by 15 inches.

a.Express the volume in terms of x.

b.Find the maximum volume, correct to the nearest tenth of a cubic inch.

c.What are the length, width and height of the box with maximum volume? Give each correct to the nearest tenth of an inch.

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.

XO=___

Find the volume and the total surface area of each solid in terms of the given variables.
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