To find the base edge of a regular triangular pyramid, we first need to find the area of the base. We can do this by rearranging the formula for the volume of a pyramid, which is V = 1/3 * base area * height.

Step 1: Rearrange the formula to solve for base area
Base area = 3 * V / h
Substitute V = 187.06 cubic meters and h = 9 meters into the formula:
Base area = 3 * 187.06 / 9 = 62.35333333 square meters

Step 2: The base of a regular triangular pyramid is an equilateral triangle. The formula for the area of an equilateral triangle is A = (s^2 * sqrt(3)) / 4, where s is the length of a side. Rearrange this formula to solve for s:
s = sqrt((4 * A) / sqrt(3))
Substitute A = 62.35333333 square meters into the formula:
s = sqrt((4 * 62.35333333) / sqrt(3)) = 12.12435565 meters

So, the minimum base edge of the regular triangular pyramid is approximately 12.12 meters.

Question

To find the base edge of a regular triangular pyramid, we first need to find the area of the base. We can do this by rearranging the formula for the volume of a pyramid, which is V = 1/3 * base area * height.

Step 1: Rearrange the formula to solve for base area
Base area = 3 * V / h
Substitute V = 187.06 cubic meters and h = 9 meters into the formula:
Base area = 3 * 187.06 / 9 = 62.35333333 square meters

Step 2: The base of a regular triangular pyramid is an equilateral triangle. The formula for the area of an equilateral triangle is A = (s^2 * sqrt(3)) / 4, where s is the length of a side. Rearrange this formula to solve for s:
s = sqrt((4 * A) / sqrt(3))
Substitute A = 62.35333333 square meters into the formula:
s = sqrt((4 * 62.35333333) / sqrt(3)) = 12.12435565 meters

So, the minimum base edge of the regular triangular pyramid is approximately 12.12 meters.

Knowee AI · Accepted Answer

To find the base edge of a regular triangular pyramid, we first need to find the area of the base. We can do this by rearranging the formula for the volume of a pyramid, which is V = 1/3 * base area * height.

Step 1: Rearrange the formula to solve for base area
Base area = 3 * V / h
Substitute V = 187.06 cubic meters and h = 9 meters into the formula:
Base area = 3 * 187.06 / 9 = 62.35333333 square meters

Step 2: The base of a regular triangular pyramid is an equilateral triangle. The formula for the area of an equilateral triangle is A = (s^2 * sqrt(3)) / 4, where s is the length of a side. Rearrange this formula to solve for s:
s = sqrt((4 * A) / sqrt(3))
Substitute A = 62.35333333 square meters into the formula:
s = sqrt((4 * 62.35333333) / sqrt(3)) = 12.12435565 meters

So, the minimum base edge of the regular triangular pyramid is approximately 12.12 meters.

A regular triangular pyramid has an altitude of 9 meters and a volume of 187.06 cubic meters. What is the minimum base edge in meters?

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