Answer to Question #103492 in Geometry for Nealy

Question

A tube for a water slide is cylindrical. The tube is 40 yards long and has a radius of 2 yards. Find the surface area. Do not include the open ends.

Answer 1

Radius of tube (r) = 2 yards

Length of tube (L) = 40 yards

Excluding open ends

Surface area of cylinder = $2\pi rL$

= $2 \pi (2 yards)(40 yards)$

= $160\pi \space cubic\space yards$

Conceptual way (if you don't remember the formula for surface area)

Consider above image which is representing cylindrical water slide tube.

Since both ends are open, if we cut the cylinder along its length and unfold it, it will turn into a rectangular sheet having length L and width equal to perimeter of the circular end.

Now as we know area of rectangle $= length * width = L * 2\pi r$ = $2 \pi rL$

Thus surface area of cylinder with open ends = $2\pi rL$

= $2 \pi (2\space yards)(40\space yards)=160\pi \space cubic \space yards$

Note: if both ends are not open then we will add $(2 *\pi r^2)$ to the above formula where $\pi r^2$ is nothing but area of each circular end.