What is the height of a cylinder with a radius of 6 inches and a surface area of 168pi in^2?
the formula should be
s = 2piRH + 2piR^2
I follow your method and find the
H = 8. Thanks.
You're right. Senior moment.
Area = 2 pi R^2 + 2 pi R H = 168 pi
72 pi + 12 pi H = 168 pi
12 pi H = 96 pi
H = 8
Good work!
To find the height of a cylinder with a given radius and surface area, we need to use the formula for the surface area of a cylinder, which is:
Surface Area = 2πr^2 + 2πrh
Given that the surface area of the cylinder is 168π in^2 and the radius is 6 inches, we can substitute these values into the formula:
168π = 2π(6^2) + 2π(6h)
Simplifying:
168π = 72π + 12πh
We can cancel out π from both sides, as it is a common factor:
168 = 72 + 12h
Rearranging the equation to isolate h:
12h = 168 - 72
12h = 96
Dividing both sides by 12:
h = 8
Therefore, the height of the cylinder is 8 inches.
Area = 2 pi R^2 + pi R H
Substitute 6 for R.
Area = 72 pi + 6 pi H
= 168 pi
Therefore
96 pi = 6 pi H
and
H = 16 (inches)