Find the circumferece of the base of a cylinder whose volume is 36 and height 4
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
v = volume
r= radius of the base
Given V = 36 and h = 4
==> 36 = r^2 * pi * 4
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.)
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.
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.