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
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.