The surface of a right cylinder is 324 pi cm^2. If the radius and height are equal, find the length of the diameter

The length of the diameter is 18 cm

Step-by-step explanation:

In this question, we are asked to calculate the diameter of a right cylinder, given that the radius and the height are equal and given the value of the surface area.

Mathematically, the surface area of a cylinder can be represented by the equation;

A = 2 π r (r + h)

since r = h, we can say h = r

Thus, the equation becomes;

A = 2 π r (r + r)

A = 2 π r (2r)

A = 4 π r^2

From the question, we can see that the value of A = 324 π

substituting this, we have;

324 π = 4 π r^2

4r^2 = 324

r^2 = 324/4

r^2 = 81

r = root of 81

r = 9 cm

The value of the diameter is two times the radius

Hence D = 2r = 2 * 9 = 18 cm