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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鈥夆赌塽苍颈迟3

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掳 for the height of the hexagonal pyramid.

h=(产补蝉别鈥塭诲驳别)脳tan50掳=4脳tan50掳=4tan50掳

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掳 for h in the formula for volume of pyramid.

V=13Bh=13(243)(4tan50掳)=323tan50掳

Substitute1.191 fortan50掳 in the formula for volume.

V=323tan50掳=32脳3脳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

If the length and width of a rectangular solid are each decreased by 20%, by what percent must the height be increased for the volume to remain unchanged? Give your answer to the nearest whole percent.

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

Rhombus with diagonals 6 and 8, h = 9.

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All nine edges of right triangular prism are congruent. Find the length of these edges if the volume is543鈥夆赌塩尘3.

Refer to cubes with edges of length e. Complete the following table.

eT.A.V64
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