What is the ratio of the sum of surface area of cylinder that its base radius is $r$ and height is $2r$ to the sectional area parallel to the base?

Question

What is the ratio of the sum of surface area of cylinder that its base radius is $r$ and height is $2r$ to the sectional area parallel to the base?

I currently don't have any idea about the question. Can you take a look?

I've tried dividing surface area to the sectional area.

$$\frac {2\pi rh}{\pi r^2}$$

However, it doesn't seem correct.

Kindest Regards!

Answer 1

Let's go step by step.

The base of the cylinder is a disk. The area of the disk is $r^2\pi$. Can you see that any section's area parallel to the base has the same area?

Now whhat is the surface area of the cylinder? Twice the base area plus the side area, right? The base is just a disk, while the side is just a rectangle, when you open it up. Therefore we have:

$$A = 2r^2\pi + 2r\pi \cdot h = 2r^2\pi + 4r^2\pi = 6r^2\pi$$

Can you derive the ratio on your own now?

Answer 2

Hint. The total surface area of the cylinder is $2\pi rh+\pi r^2+ \pi r^2$ where $h=2r$.