Question

PLEASE HELP!

Answer 1

you need to look for the formula of the surface area of the cylinder first.
Do you have it?

Answer 2

no

Answer 3

Do you consider a closed cylinder? or just a tube? this makes a difference for the area, you must know if you must consider the area of the two discs above and below as well.

Answer 4

its a closed cylinder

Answer 5

Then, the total area is: area of the 2 discs + area of the side (whic, unfolded, looks like a rectangle).
If the radius is \(r\) and the height is \(h\), the area is then:
\[
2\times (\text{area of disc}) + \text{area of rectangle} = 2\times(\pi r^2)+ 2\pi r h
\]
where \(2\pi r \times h\) is : length of the rectangle \(\times\) width of the rectangle.
In your problem, \(h=2r\).

Answer 6

length of the rectangle is \(2\pi r\) because if you look well, it corresponds to the perimeter of the disc.

Answer 7

so how would I find the diameter of the base?

Answer 8

You are given the area: \(56\pi\).
You know the formula is \(2\pi r^2 + 2\pi rh \) where \(h=2r\).
So you need to find the value of \(r\) such that\[ 2\pi r^2 + 2\pi r 2 r = 56\pi\].

Answer 9

what about the next question?