How to find the surface area of a cylinder with a diameter of 6ft and a height of 20cm using 3.14 rounded to the nearest whole number. (I cant figure it out my book doesn't give an example of it just a radius formula and ive tried searching the formula but i cant find any websites that show me how to do it or whats the formula)

Question

whpalmer4 · Answer

Well, the radius is just half of the diameter, right?

whpalmer4 · Answer

Surface area of the cylinder is the area of the two ends + the area of the sides.  

The two ends are circles of radius $r$:$$A_{ends} = 2*\pi r^2$$ (the 2* is because there are two of them)

The surface area of the side is found by slicing the cylinder down the side and unrolling it into a rectangle of height $h$ and width $2\pi r$ (which you should recognize as the circumference of the circle that makes up the ends).  
$$A_{sides} = 2\pi r h$$(just length * width)

$$A = 2\pi r^2 + 2\pi r h$$for the whole surface of the cylinder.

Finally, $$r = \frac{d}{2}$$

If you really want a formula for surface area based on diameter, you could substitute $r = \frac{d}{2}$ into that equation:
$$A = 2\pi (\frac{d}{2})^2 + 2\pi(\frac{d}{2})h = \pi\frac{d^2}{2} + \pi d h$$