Question

I really need help, I'll do almost anything for help ;)

Answer 1

Use the net to find the surface area of the cylinder

Answer 2

Well, when you 'open' the cylinder the side becomes simply a rectangle.
One side of that rectangle is the height (13m in your example) and the other is the perimeter of the base. Let's start by finding this rectangle's area. can you do that? =)

Answer 3

Answer choices

About 273 m^2
About 179 m^2
About 302 m^2
About 151 m^2

Answer 4

Well, do you want to solve it or just the solution?

Answer 5

both

Answer 6

ok, so first tell me if you can do the first step as described in my first reply

Answer 7

Can you just show me how to do it and put the answer at the end, please I'll do anything!?!

Answer 8

you can just send me the answer now, and post how to slove it later

Answer 9

please

Answer 10

Well, the surface of the cylinder is basically the sum of areas of its components.
The cylinder is built from 2 circular bases (which are equal) and the side that connects which is basically a rectangle rolled around them.

The area of the rectangle is simply the length*height.
We know that the height is 13m.
Since the rectangle is rolled around the base, we know it shares a side with the base's perimeter.
That means that the 'length' side is in the same length as the perimeter of the base.

To find the perimeter we can use the number \(\pi\) which stands for the ratio between the perimeter and the diameter of a circle.
The diameter of the base is basically twice its radius (which is 3m), so we get:
$$
\text{base_perimeter} = \pi \cdot (2 \cdot 3_m) = \pi6_m \\
\text{cylinder_side_area} = \text{cylinder_height} \cdot \text{base_perimeter} = \\
= 13_m \cdot \pi6_m = \pi(13_m \cdot 6_m) = \pi78_{m^2}
$$

To that area we have to add the area of both the bases.
The bases are equal and circular. Each base's area can be calculated by the circle area formula \(\pi r^2\) (where \(r\) is the radius of the circle, which is 3m in our case)
so:
$$
\text{base_area} = \pi \cdot (3_m)^2 = \pi 9_{m^2}
$$ And now the surface is basically the total area of all the parts:
$$
\text{cylinder_surface} = \text{side_area} + 2 \cdot \text{base_area} = \\
= \pi78_{m^2} + 2 \cdot \pi 9_{m^2} = \pi (78_{m^2} + 18_{m^2}) = \pi 96_{m^2} \approx 302_{m^2}
$$