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What is the circumference of the base of a cylinder if given the volume is 48 and the...

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calraedwards | Student, College Freshman | (Level 2) eNoter

Posted April 21, 2011 at 5:06 AM via web

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What is the circumference of the base of a cylinder if given the volume is 48 and the height is 7 ( I need the answer in terms of pi ).

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

Posted April 21, 2011 at 5:41 AM (Answer #1)

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Given the volume of the cylinder is 48 and the height is 7.

We will use the volume of a cylinder formula to find the radius of the base.

==> V = r^2 * pi * h

==> 48 = r^2 * pi * 7

==> r^2 = 48/7pi =

==> r= sqrt(48/7pi)= 4sqrt(3/7pi)

Now we will calculate the circumference of the base.

==> C = 2* r * pi = 2*4sqrt(3/7pi) * pi

==> C = 8 sqrt(3/7)* sqrtpi

==> C = 8 sqrt(3pi/7)

Then the circumference of the base is C= 8sqrt(3pi/7) units.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 21, 2011 at 5:41 AM (Answer #2)

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The volume of a cylinder is given by pi*r^2*h where h is the height and pi*r^2 is the area of the base.

Here the volume is 48 and the height is 7

=> pi*r^2 = 48/7

r^2 = 48/(7*pi)

r = sqrt (48/7*pi)

The circumference is 2*pi*r

=> 2*pi*sqrt (48/7*pi)

The circumference of the base is 2*pi*sqrt (48/7*pi)

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