# A Bright Library

**Geometry**Level 4

Consider a light bulb on the top of a library. It is \(20 \text{ m}\) above the ground and, horizontally, \(5 \text{ m}\) from a wall. Consider that the recipe that contains the light bulb is a conical frustum with a greater diameter of \(8 \text{ cm}\) , height of \(2 \text{ cm}\) and smaller diameter of \(4 \text{ cm}\). Take the recipe to be opaque to light. How far from the ground, in meters, is the highest point of the wall that can be illuminated by the light bulb?

**Details and Assumptions**:

The light bulb is right in the middle of the recipe's smaller base. Take the bulb to be a punctate body.

The smaller diameter is the diameter of the frustum's smaller base, and the greater diameter is the diameter of the frustum's greater base.