find the height of the rsquare based prisim if you know that area of base is 36m and volume is 288 m^3

Expert Answers
hala718 eNotes educator| Certified Educator

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)

Now substitute:

==> 288 = 36 * h

Now divide by 36

==> h = 288/ 36

           = 8

==> the height of the prisim is 8 m

giorgiana1976 | Student

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

neela | Student

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