4. Find the volume of the pyramid. Round to the nearest tenth.
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1 point
9 mi 6mi 7 mi
54 mi^3
312.4 mi^3
63 mi^3
126 mi^3
To find the volume of a pyramid, we use the formula V = (1/3) * base area * height.
First, we need to find the base area. The base of the pyramid is a triangle with side lengths 9 miles, 6 miles, and 7 miles. We can use Heron's formula to find the area of this triangle.
s = (9 + 6 + 7) / 2 = 11
area = √(s(s-9)(s-6)(s-7)) = √(11(11-9)(11-6)(11-7)) = √(11(2)(5)(4)) = √(440) ≈ 20.976
Now, we can use the volume formula to find the volume:
V = (1/3) * base area * height = (1/3) * 20.976 * 6 = 41.952 ≈ 42
Rounding to the nearest tenth, the volume of the pyramid is 42 mi^3.