# 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.

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