Find the volume of the cylinder whose height is 7 and the circumference of the base is 4.

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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

=>...

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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.

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An illustration of the letter 'A' in a speech bubbles

 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.

Approved by eNotes Editorial Team