Question

31.What is the surface area of the cylinder?

Answer 1

Hello there. To solve this question, we'll have to remember some properties about cylinders.

We want to determine the surface area of the following cylinder:

In this case, the surface area comprehends the bottom, the top and the lateral area of the cylinder.

For a cylinder with height h and radius R, it is easy to show that

By redrawing the cylinder as the following figures:

Notice the 2pi * R came from the measure of the circumference of the top and bottom circles.

The area of the circles are given as

`\pi\cdot R^2`

And the area of the rectangle is

`2\pi Rh`

So the surface area of this cylinder is given as

`2\pi R^2+2\pi Rh`

Plugging the values R = h = 1.5 m, we'll get

`2\pi\cdot1.5\cdot(1.5+1.5)=9\pi\approx28.27\text{ m}^2`

In this case, the answer is 9pi and it is contained in the 4th option.