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What is the volume of a frustum of a rectangular pyramid if one base has measurements 6 ft. × 8 ft., the other base has measurements 14 ft. × 18 ft., and the height is 3 ft.? A. 120.98 ft.3 B. 560.30 ft.3 C. 409.98 ft.3 D. 252.8 ft.3

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sqdancefan

Answer:

C. 409.98 ft³

Explanation:

The formula for the volume of a frustum is ...

... V = (h/3)(B₁ + √(B₁B₂) + B₂)

where B₁ and B₂ are the areas of the bases.

Here, we have ...

... B₁ = (6 ft)(8 ft) = 48 ft²

... B₂ = (14 ft)(18 ft) = 252 ft²

So the volume is ...

... V = (3 ft)/3 × (48 ft² + √(48·252) ft² + 252 ft²) ≈ 409.98 ft³

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