find the height of the rsquare based prisim if you know that area of base is 36m and volume is 288 m^3
We know that the volume of the prisim is:
V = Length * width* height
But the base is square.
==> Lenth * width = x^2 = area of the base
==> V = area of the base (a) * height (h)
==> 288 = 36 * h
Now divide by 36
==> h = 288/ 36
==> the height of the prisim is 8 m
First, I'll make a correction!
The area of the base is 36 m^2 and not 36m, as in enunciation.
Now, we'll enunciate the formula of the volume of the prism supposing that is a right regular prism with the square base, which is called regular right rectangular prism.
V = A base * height of prism
We'll substitute the known values into the formula:
288 m^3 = 36m^2 * height of prism
height of prism = 288 m^3 / 36m^2
We'll eliminate the like terms:
height of prism = 8 m
A right prism is a 3 dimensional solid having identical top and bottom polygonal surfaces connected by rectangular surfaces which are perpenducular to both top and bottom surfaces.
The volume V of the right prism is equal to the product of the area A of bottom(or top) surface and the height h of the prism.
So V = Ah....(1)
Given V = 288 m^3 and A =36 m^2. Substituting in (1), we get :
288 m^3= (36m^2)h
h = 288 m^3/36m^2 = 8m.
So height of prism is 8m