Find the circumferece of the base of a cylinder whose volume is 36 and height 4

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the circumference of the base of a cylinder whose volume is 36 and height 4.

Now for a cylinder with a radius of r and height h, the volume is pi*r^2*h

We have height given as 4 , volume is 36

=> 36 = pi*r^2*4

=> pi*r^2 = 9

=> r^2 = 9 / pi

=> r = sqrt ( 9 / pi)

Therefore the circumference of the base is 2*pi*r

=> 2*pi*sqrt(9 / pi)

=> 2*3* sqrt pi

=> 6 sqrt pi.

The required circumference is 6 sqrt pi.

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

Posted on

The cylinder has volume of 36 and height 4.

Then we know that the formula for the cylinder volume is:

 V = r^2 *pi * h

Where :

v = volume

h= height

r= radius of the base

Given V = 36   and h = 4

==> 36 = r^2 * pi * 4

Then :

r^2 = 36/ 4pi

==> r^2 = 9/pi

==> r= 3/sqrt(pi)

Now we will calculate the circumference of the base by using the formula:

C = 2*r*pi

==> C = 2* (3/sqrt(pi)  * pi

==> C = 2*3*sqrt(pi)

==> C = 6sqrt(pi)

==> C = 10.63 ( approx.)

 

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

The volume of the cylinder = 36 and its height = 4. We have to find the circumference of the cylinder:

The volume V of a cylinder is given by :

V = Pi*r^2*h, where r is radius of the cylinder and h is the height of the cylinder.

Put the given values  V = 36 and h = 4 to find the radius r in Pi*r^2*h = V.

pi* r^2*4 = 36.

Therefore r^2 = 36/4pi = 9/pi.

Thetrefore r = sqrt(9/pi)  = 3/sqrtpi.

Therefore  the corcumference of the cylinder = 2pi*r = 2p* (3/sqrtpi) = 6 sqrtpi = 10.6347 nearly.

Therefore the circumference of the cylinder = 10.6347 nearly.

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