Question

The diameter of the base of the cylinder is 8 and the volume is 64π. 1) Find the surface area of the base of the cylinder. 2) Find the height of the cylinder. 3) Find the area of the lateral surface of the cylinder.​

Answer 1

Пошаговое объяснение:
The surface area of the base of the cylinder is given by the formula: A = πr^2, where r is the radius of the base. Since the diameter of the base is 8, the radius is half of that, so r = 8/2 = 4. Plugging this value into the formula, we have:

A = π(4^2) = 16π.

The volume of the cylinder is given as 64π, which can be expressed as V = πr^2h, where h is the height of the cylinder. We need to find the value of h. Rearranging the formula, we have:

64π = π(4^2)h

64 = 16h

h = 64/16

h = 4.

So, the height of the cylinder is 4 units.

The lateral surface area of a cylinder is given by the formula: A = 2πrh. Substituting the known values, we have:

A = 2π(4)(4) = 32π.

Therefore, the area of the lateral surface of the cylinder is 32π square units.