Question

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.

Explanation:

Step1: Calculate sphere surface area

The formula for the surface area of a sphere is $4\pi r^2$.

Step2: Calculate cylinder surface area

The total surface area of a cylinder is $2\pi r^2 + 2\pi rh$. Substitute $h=r$:

$$\begin{align*} 2\pi r^2 + 2\pi r(r) &= 2\pi r^2 + 2\pi r^2\\ &= 4\pi r^2 \end{align*}$$

Step3: Compare the two surface areas

Both the sphere and cylinder have a surface area of $4\pi r^2$, so they are equal.

Answer:

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