Given the volume of the cylinder is v=39 in^3
We will use the formula of the cylinder volume to solve.
We know that:
V = r^2 *pi * h such that v is the volume, r is the radius, and h is the height.
We are given the volume and the height.
Then we will substitute into the equation.
==> 39 = r^2*pi * 12
Now we will divide by 12.
==> r^2 *pi = 39/12 = 3.25
But we know that the area of the base is given by :
A = r^2 * pi
Then, the area of the base of the cylinder is 3.25 in^2
The volume of a cylinder is given in terms of the area of the base of the cylinder(a) and the height (h) of the cylinder by the formula V = A*h.
For a cylinder with volume 39 square inch and height 12 inches, the volume is 39 = 12* a
This gives a = 39/12.
The area of the base is 39/12 square inches.
The base area of a cylinder is A = pir^2, where r is the radius.
The volume v of the cylinder is given by pir^2*h , where h is the height of the cylinder.
So given v = 39 in^3 and h. = 12 in.
Therefore v = pir^2*12 = 39.
We divide both sides of pr^2*12 = 39 by 12 and get:
So pi*r^2 = 39/12 = 3.25 sq inch.
Therefore the area of the base of the cylinder A = pir^ = 3.25 sq in.