Find the height of a cylinder with a radius of 4 centimeter and the surface area is 72pi?

Answer 1

Think of the surface area of the cylinder in three parts. The top, the bottom, and the side. Surface area of the top and the bottom are easy, because the area of a circle is pi times the radius squared. Since the radius is 4, the area of the top and bottom are 16*pi each for a total of 32*pi.

This means that the surface area of the "tube part" is 40*pi. {72 - 32 = 40}

If you think of cutting this part, you can see that it's really just a rectangle. One side of the rectangle is the height of the cylinder, the other is the circumference of the base. The circumference is 2*pi*r, which here is 8*pi.

Thus (8*pi)(height of cylinder) = (40*pi). Conclusion, the height of the cylinder is 5 cm.