Given that the base of a square based prism is x cm and the height is h cm, find an equation for h in terms of x.I dont get the wording of it and how to solve it.
We know that the volume of the prisim is:
V = area of the base (a)* height (h)
But we know that the area of the base = x^2
Given the volume we will have:
V = x^2 * h
==> v = (x^2)*h
Now we need h on one side by itself, so we divide by x^2
==> V / x^2 = h
==> h = V/x^2 (given the volume)
To determine the height of a right prism with a square base it should be given the base area and volume of the prism, or some information related with lareral surfaces.
So we pressume that the right prism of square base has the base side x and volume V and the height h.
The volume is equal to base area*height. Or
V = x^2*h.To make h subject, we need to isolate h by dividing both sides by x^2:
V/x^2 = h.
h = V/x^2...(1)
Example: Suppose the side of the square base is 6cm and volume is 288cm^3, then height h is given by substituting values in formula at (1):
h = V/x^2 = 288cm^3/(6cm)^2 = 288cm^3/36cm^2 = 8cm