Question

The volume v of a rectangular pyramid varies jointly with the area of the base b and the height h. v = 36 m3 when b = 27 m2 and h = 4 m. identify b when v = 32 m3 and h = 12 m.

Answer 1

The base b is  8 m².

Given in the problem, if the volume V of a rectangular pyramid varies jointly as the area of the base b and the height h, you can write the following equation:

v = kbh ,k is constant

36 m³ =k27 m² x4 m

k = 0.33

When v = 32 m³ , b = ? , h =  12m

v = kbh

b = v / kh

b = 32/ 0.33 x 12

b = 32/4 = 8 m²

b =  8 m²

Therefore, the base is  8 m².

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