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

Answer: B=27 m²

Step-by-step 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:

$k=\frac{1}{3}$

Then, when V=81 m³ and h=9m m, B is:

$V=kBh\\B=\frac{V}{kh}\\B=\frac{81m^{3}}{\frac{1}{3}*9m}\\B=27m^{2}$

Answer 2

Answer:

B = 27 m² is the answer.

Step-by-step 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