Question

A sphere with radius r and a cylinder with radius r and a height of r are shown below. How do the surface areas of these solid figures compare? Which statements are correct? Check all that apply. The surface area of the sphere in terms of r is 4πr2 square units. The surface area of the cylinder in terms of r is 4πr2 square units. The surface area of the cylinder in terms of r is 6πr2 square units. The surface area of the cylinder and sphere are the same. The surface area of the cylinder and sphere are not the same.

Answer 1

• The surface area of the sphere in terms of r is 4πr^2 square units.
• The surface area of the cylinder in terms of r is 4πr^2 square units.
• The surface area of the cylinder and sphere are the same.

Explanation:

The surface area of the sphere is given by the formula ...

A = 4πr^2

The surface area of the cylinder is given by the formula ...

A = 2πr^2 +2πrh

Here, the height (h) is equal to r, so this simplifies to ...

A = 2πr^2 +2πr·r = 4πr^2 . . . . . the same area as the sphere