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The volume of a pyramid varies jointly with its height and the area of its base. A pyramid with a height of 16 feet and a base area of 78 square feet has a volume of 416 cubic feet. If a pyramid has a base area of 102 square feet and a volume of 238 cubic feet, find its height.

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Answer:

7 ft

Step-by-step explanation:

base is b feet on each side

area of base is b² square feet

height is h feet

volume varies jointly with h and b²

V = kb²h

416 = k·78·16

k = ⅓

V = ⅓b²h

b² = 102

V = 238

h = 3V/b² = 7 ft

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