Question

The volume V of a rectangular pyramid varies jointly as the area of the base B and the height h. V = 56 m3, when B = 24 m2 and h = 7 m. Identify B when V = 81 m3 and h = 9 m.

Answer 1

B = 27 m² is the answer.

Explanation:

Volume of a rectangular pyramid is = V

Area of the base is B and the height of pyramid is h.

We have to find the value of B

If V = 56 m³ then B was = 24 m²and h = 7 m

Now if V = 81 m³ and h = 9 m then from the formula of volume of a pyramid is V = 1/3(B×h) = 81 m³

81 = 1/3(B×9)

B = (81×3)/9 = 81/3 = 27 m

Answer 2

Answer: B=27 m²

Explanation:

Based on the information 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`

Where k is a constant.

You can calculate k as following:

`56m^(3)=k*24m^(2)*7m`

When you solve for k you obtain:

`k=(1)/(3)`

Then, when V=81 m³ and h=9m m, B is:

`V=kBh\\B=(V)/(kh)\\B=(81m^(3))/((1)/(3)*9m)\\B=27m^(2)`