# The volume of the cylinder is 45п cm³, and the base area is 9п cm². find the area of the lateral surface of the cylinder.

January 28, 2021 | education

| Given:

cylinder;

V = 45Pi cm ^ 3;

Soc. = 9Pi cm ^ 2;

To find:

Sb.p. =?

Decision:

The area of the lateral surface of the cylinder is found by the formula:

Sb.p. = 2 * Pi * R * H.

To do this, you need to find the centering radius and the height of the cylinder.

V = Soc. * H;

Let’s find the height.

45Pi = 9Pi * H;

H = 45Pi / 9Pi = 5 cm.

Now let’s find the radius of the base:

Soc. = Pi * R ^ 2;

9Pi = Pi * R ^ 2;

R ^ 2 = 9Pi / Pi = 9;

R = 3cm.

Substitute the values for the radius and height, and find the area of the side surface:

Sb.p. = 2 * Pi * R * H = 2 * Pi * 3 * 5 = 30Pi cm ^ 2.

Answer: Sb.p. = 30Pi cm ^ 2.