Hi Lorne.

The surface area of the main "open-ended" cone is the same as the surface area of a full (closed) cone minus the surface area of the cone that is a cap on the top.

The surface area S of a cone is calculated based on the height h and the radius r at the base:

So we need to find these quantities first.

Notice that the cross-section shown here reveals the similar triangles involved in the geometry.

In similar triangles, the ratios of the side lengths is the same. This means that 10/7 = h/8. Thus, the h = 80/7 ft.

If we use the formula for surface area above with r = 8 and h = 80/7, we can calculate the surface area of the full large (closed) cone. The surface area of the cap would come from using r = 1 and h = 80/7 - 10.

Subtract these surface areas to complete the problem.

Cheers,
Stephen La Rocque.