Find the height of the cylinder, to the nearest tenth, if the volume is 231 and the circumference of the base is 8pi

Expert Answers
hala718 eNotes educator| Certified Educator

Given that the volume of a cylinder is 231.

Then we know that:

v = r^2 * pi * h such that r is the radius and h is the height.

But we are given that the circumference of the base is 8pi.

==> C = 2* pi *r = 8pi

=> r = 8pi/2pi = 4

Then the radius of the base is 4 .

Now we will substitute the volume and radius into the equations.

==> v= r^2 * pi * h

==> 231 = 4^2 * pi * h

==> h = 231/ 16pi = 4.6

Then the height , to the nearest tenth, is 4.6 units.

justaguide eNotes educator| Certified Educator

The volume of a cylinder is given by pi*r^2*h where h is the height and r is the radius if the base.

Here pi*r^2*h = 231

Circumference of the base = 2*pi*r = 8*pi

=> r = 4

pi*16*h = 231

=> h = 231 / 16*pi

=> h = 4.59

The required height is 4.6