Question

Find the surface area of a cylinder tank with a circular top and bottomwith radius 15 feet and height 40 feet.

Answer 1

To calculate the surface area of a cylinder, we need first to notice that the side part of it is equivalent to a rectangle:

The dimensions of the rectangle will be the cylinder height by the length of the circunference of the base/top.

Thus, the surface area will be the sum of the areas of the base and the top and the rectangle.

The area of the base and the top are the same and are the area of a circle of radius 15 feet, so:

`A_c=\pi r^2=\pi15^2=225\pi`

And for the area of the rectangle, we first need the circunference of the base/top:

`C=2\pi r=2\pi\cdot15=30\pi`

Now, we can multiply by the height to get the area of the rectangle:

`A_r=h\cdot C=40\cdot30\pi=1200\pi`

Now, we add the three:

`A_t=A_c+A_c+A_r=225\pi+225\pi+1200\pi=1650\pi\approx5183.63`

So, the surface area is 1650π feet or approximately 5183.63 feet.