We are given the circumference of the base as equal to 4 and the height is 7.
We have to find the volume.
Now we first find the area of the base. Let the radius of the base be r.
As the circumference is 4.
=> 2*pi*r = 4
=> r = 2/ pi
Area = pi*r^2
=> pi * 4 / pi^2
=> 4 / pi.
The volume of the cylinder is (4/ pi)*height = (4/ pi)*7 = 28/pi.
Therefore the required volume is 28/pi.
We know that the volume of the cylinder is:
V = r^2 * pi * h where r is the radius and h is the height.
Given that the height is h = 7
==> V = r^2 * pi * 7
Now to determine the radius ( r), we will use the circumference formula.
We know that the circumference of a circle is given by the formula:
C = 2* pi * r
Given C = 4.
==> 2* pi *r = 4.
==> r= 4/2pi = 2/pi.
==> r= 2/pi.
==> V = ( 2/pi)^2 * pi * 7.
==> V = 4/pi * 7 = 28/p.i
Then, the volume of the cylinder is 28/pi cubic units.
The volume of the cylinder whose radius is r and height is h is given by:
V = pr^2h...(1)
The relation between the circumference and the radius is given by:
r = C/2pi , where C is the circumference.
In this case circumference = 4. So r = 4/2pi..
Therefore we substitute r = 4/pi in the volume formula at (1) and height h = 7 as in the data given.
So the volume of the cylinder = pir^2*h = pi (4/2pi)^2 * 7 = 8.9127 cubic units.
So the volume of the cylinder = 8.9127 cubic units.