What is the circumference of the base of a cylinder if given the volume is 48 and the height is 7 ( I need the answer in terms of pi ).
Given the volume of the cylinder is 48 and the height is 7.
We will use the volume of a cylinder formula to find the radius of the base.
==> V = r^2 * pi * h
==> 48 = r^2 * pi * 7
==> r^2 = 48/7pi =
==> r= sqrt(48/7pi)= 4sqrt(3/7pi)
Now we will calculate the circumference of the base.
==> C = 2* r * pi = 2*4sqrt(3/7pi) * pi
==> C = 8 sqrt(3/7)* sqrtpi
==> C = 8 sqrt(3pi/7)
Then the circumference of the base is C= 8sqrt(3pi/7) units.
The volume of a cylinder is given by pi*r^2*h where h is the height and pi*r^2 is the area of the base.
Here the volume is 48 and the height is 7
=> pi*r^2 = 48/7
r^2 = 48/(7*pi)
r = sqrt (48/7*pi)
The circumference is 2*pi*r
=> 2*pi*sqrt (48/7*pi)
The circumference of the base is 2*pi*sqrt (48/7*pi)