Help please solve this problem for algebra

Question

The volume V of a pyramid varies jointly as the area of it’s base B and its height h. If the volume of the pyramid is 24 cubic meters when the area of it’s base is 18 square meters and its height is 4 meters find the volume of a pyramid when the area of it’s base is 21 square meters and its height is 7 meters.

Answer 1

I would do this as a proportionality problem:

V = 1/3 Ah where A is the area of the base and h is the height.

V_i = 1/3 A_ih_i for any case i , so if we are given all the values for case 1 and need one of the values for case 2 you can use the proportion:

V₂/V₁ = (A₂/A₁)(h₂/h₁) or

V₂= (24 m³)(21m²/18m²)(7 m/4 m) This is like the combined gas law in chemistry. Note that the units need only be consistent within the parentheses.

Good luck!