Question

The volume of this regular pentagonal pyramid is 82.5 cubic meters. What is the height of the pyramid?

Answer 1

the height of the pentagonal pyramid is 5. 70 meters

Volume of a regular pentagonal pyramid

The formula for determining the volume of a regular pentagonal pyramid is given as;

V=5/12tan(54°)ha^2

Where

• a is the base edge
• h is the height

We have the volume to be;

volume = 82. 5 cubic centers

height = h

a = 5m

Substitute the values

$82. 5 = \frac{5}{12}$ × $tan 54$ × $h$ ×$5^2$

$82. 5 = 0. 42$ × $1. 3764$ × $25$ × $h$

Make 'h' subject of formula

$h = \frac{82. 5}{14. 45}$

h = 5. 70 meters

The height of the pentagonal pyramid is 5. 70 meters

Thus, the height of the pentagonal pyramid is 5. 70 meters

Learn more about a pentagonal pyramid here:

brainly.com/question/16315924

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