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Math  /  Geometry

QuestionThe base of the pyramid in the diagram is a regular hexagon. The length of each side of the hexagon is 6 ft and the height of the pyramid is 6 ft . The area of the regular hexagon is 93.5ft293.5 \mathrm{ft}^{2}. What is the volume of the pyramid? Round your answer to the nearest cubic foot.

Studdy Solution

STEP 1

1. The base of the pyramid is a regular hexagon.
2. Each side of the hexagon measures 6 6 feet.
3. The height of the pyramid is 6 6 feet.
4. The area of the hexagonal base is 93.5 93.5 square feet.

STEP 2

1. Recall the formula for the volume of a pyramid.
2. Substitute the given values.
3. Calculate the volume.
4. Round the volume to the nearest cubic foot.

STEP 3

Recall the formula for the volume of a pyramid:
V=13×Base Area×Height V = \frac{1}{3} \times \text{Base Area} \times \text{Height}

STEP 4

Substitute the given values into the formula:
V=13×Base Area×Height V = \frac{1}{3} \times \text{Base Area} \times \text{Height} =13×93.5ft2×6ft = \frac{1}{3} \times 93.5 \text{ft}^2 \times 6 \text{ft}

STEP 5

Calculate the product:
V=13×93.5ft2×6ft V = \frac{1}{3} \times 93.5 \text{ft}^2 \times 6 \text{ft} =13×561ft3 = \frac{1}{3} \times 561 \text{ft}^3 =187ft3 = 187 \text{ft}^3

STEP 6

Round the volume to the nearest cubic foot:
The volume is already a whole number, so no rounding is necessary.
The volume of the pyramid is:
187ft3 \boxed{187 \text{ft}^3}

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