The volume of a cylinder is 720 and the height is 12. What is the circumference of the base?

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hala718's profile pic

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

Posted on

Given the volume of a cylinder is 720 and the height is 12.

We need to find the circumference of the base.

First we will need to determine the radius of the base.

We will us the volume formula to find the radius.

We know that V = r^2 * pi * h = 720

==> r^2 * pi * 12 = 720

==> r^2 = 720/12pi = 19.1 (approx.)

==> r= 4.37

Now we will calculate the circumference of the base.

We know that C = 2* pi * r = 2* pi * 4.37 = 27.46 units ( approx.)

Then the circumference of the base of the cylinder is 27.46 units.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The volume of a cylinder is given as area of the base*height.

Here volume is 720 and the height is 12.

720  = area* height = area * 12

area = 720/12

=> 60

The area of the base is given by pi*r^2, where r is the radius.

pi*r^2 = 60

=> r^2 = 60 / pi

=> r = sqrt (60/pi)

The circumference of the base is 2*pi*r

=> 2*pi*sqrt 60 / sqrt pi

=> 2*sqrt 60 * sqrt pi

=> 2* sqrt(60*pi)

The required circumference of the base is 2*sqrt(60*pi)

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