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.

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.