What is the volume of the cylinder whose height is 12 and cricumference of the base is 20?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

As the circumference of the base is 20, we have 2*pi*r = 20, where 20 is the radius of the base.

2*pi*r = 20

=> r = 10/pi

The area of the base is pi*r^2 = pi* (10/pi)^2

=> 100/pi

The volume of the cylinder is equal to area of the base* height

=> 100/pi * 12

=> 1200/pi

The required volume of the cylinder is 1200/pi

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the height of a cylinder is h= 12

Also, given the circumference of the base is c=20.

We need to find the volume.

We know that the volume of the cylinder is given by:

V = r^2 * pi * h such that r is the radius of the base and h is the height.

==> We will determine the value of r from the circumference.

We know that:

c= 2*pi*r = 20

==> r= 20/2pi = 3.18

Now we will substitute into V.

==> V = r^2 * pi * h = (3.18)^2 * pi * 12 = 381.97

Then the volume of the cylinder is 381.97 cubic units.

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