Calculate the height of the cylinder if the volume is 42 and the circumference of the base is 6pi.
Given that the volume of a cylinder is 42
Then we will write the formula of the cylinder:
V = r^2 * pi * h = 42 where r is the radius and h is the height.
Then, we need to determine the radius using the circumference of the base.
We know that the circumference is given by:
C = 2* r * pi = 6pi
==> r = 6pi/ 2pi = 3
==> r= 3
Now we will substitute into the volume.
==> r^2 * pi * h = 42
==> 9 * pi * h = 42
==> h= 42/9pi = 14/3pi = 1.49 ( approx.)
Then, the height of the cylinder is 14/3pi = 1.49 units.
The volume of a cylinder is given by the product of the area of the base and the height.
Here we have volume given as 42 and the circumference of the base is 6*pi.
The circumferance is 2*r*pi = 6*pi
=> r = 3
The area of the base is pi*r^2 = 9*pi
9*pi*height = 42
So the height is 42/ (9*pi)
=> height = (14/3)/ pi
The required height is (14/3)/pi.
The formula relating to the circumference C and volume v of the cylinder are C = 2pi*r and v = pr^2*h, where r is the radius and h is the height of the cylinder.
By data C = 6pi and v = 42.
=> 2pir = 6pi, So r = 6pi/2pi = 3.
So the radius r = 3.
Also given v = 42 => pi*r^2 h= 42
=> h =42/pi2^2 = 42/pi*3^2 = 42/9pi = 1.4854 units.
So the height of the cylinder is 1.4854 units.