Question

The volume of a pyramid varies jointly as the height and the area of the base. If a pyramid has the measurements V=1144

cubic meters, l=8 meters and w=11 meters, and h=39 meters, what is the volume of a pyramid that has a length of 15 meters, width of 46 meters, and height of 48 meters. Round your answer to the nearest hundredth.
Find the value of k ( rounded to the nearest hundredth ). Using the value of k, find an equation that represents the general relationship indicated above

Answer 1

• 11040 m³
• k ≈ 0.33
• V = (1/3)Bh

Explanation:

The given relation is ...

V = kBh . . . . . for some base area B, height h, and constant of variation k

We are given length and width of the base so we presume it is a rectangle.

B = l·w = 8·11 = 88 . . . . square meters

The given volume tells us the value of k:

1144 = k(88)(39) . . . . . . cubic meters

1144/3432 = k = 1/3 ≈ 0.33

The value of k is about 0.33.

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Then the volume of the larger pyramid is ...

V = (1/3)(15 m)(46 m)(48 m) = 11,040 m³

The general relationship is ...

V = 1/3Bh