if lateral area of a cylinder is 96\pi and the height is 12 what is the radius
We know that the lateral area of a cylinder is given by the formula:
Lateral area = 2πrh
where r is the radius and h is the height.
Substituting the given values, we get:
96π = 2πr(12)
Simplifying, we get:
r = 4
Therefore, the radius of the cylinder is 4.
The formula for the lateral area of a cylinder is given by:
Lateral Area = 2πrh
where r is the radius and h is the height.
We are given that the height is 12 and the lateral area is 96π. Substitute these values into the formula:
96π = 2πr(12)
To solve for the radius, divide both sides of the equation by 2π(12):
96π / (2π(12)) = r
Cancel out the π terms:
96 / (2(12)) = r
Evaluate the expression on the right side:
96 / 24 = r
Simplify:
4 = r
Therefore, the radius of the cylinder is 4.