The surface area of a right cylinder is 112 pi cm ^2. If the radius is 4cm, what is the height of the cylinder?
To find the height of the right cylinder, we need to use the formula for the surface area of a cylinder:
Surface Area = 2πr^2 + 2πrh
Given:
Surface Area = 112π cm^2
Radius (r) = 4 cm
Substituting the given values into the surface area formula, we have:
112π = 2π(4^2) + 2π(4)(h)
First, simplify the equation:
112π = 32π + 8πh
Combine like terms:
112π - 32π = 8πh
Simplify the equation further:
80π = 8πh
Divide both sides by 8π:
80π / 8π = h
10 = h
Therefore, the height of the cylinder is 10 cm.
To find the height of the cylinder, we can use the formula for the surface area of a right cylinder, which is given by:
SA = 2πr^2 + 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
In this problem, we are given that the surface area is 112π cm^2 and the radius is 4 cm.
Substituting these values into the formula, we have:
112π = 2π(4^2) + 2π(4h)
Simplifying the equation:
112π = 32π + 8πh
Now let's isolate the term that contains the height:
112π - 32π = 8πh
80π = 8πh
Divide both sides of the equation by 8π to solve for h:
h = (80π) / (8π)
Simplifying the expression:
h = 10 cm
Therefore, the height of the cylinder is 10 cm.
2πr(r+h) = 112π
8π(4+h) = 112π
4+h = 14
h = 10