Find the height of each pyramid. 5. square base with edge 15 feet and volume 1,350 cubic feet 6. triangular base with base edge 12 inches and base height 9 inches, and volume 108 cubic inches 7. GREAT PYRAMID The Great Pyramid has a height of about 480.7 feet and base edges about 756 feet. The base is almost square. Find the approximate volume of this pyramid.
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To find the height of the square base pyramid, you can use the formula for the volume of a pyramid, which is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of a square with edge length 15 feet is \( 15 \times 15 = 225 \) square feet. Setting the volume to 1,350 cubic feet, you rearrange the formula: \( 1,350 = \frac{1}{3} \times 225 \times \text{Height} \). Solving for height gives you approximately 18 feet. For the triangular base pyramid, the base area is the area of a triangle, calculated as \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times 9 = 54 \) square inches. Using the volume formula again, \( 108 = \frac{1}{3} \times 54 \times \text{Height} \), which results in a height of approximately 6 inches. As for the Great Pyramid, the volume can be found using the same pyramid volume formula. With a base area of \( 756 \times 756 \approx 571,536 \) square feet, you can then plug in the values: \( V = \frac{1}{3} \times 571,536 \times 480.7 \). This will yield a volume of approximately 91,389,000 cubic feet.
