Question

A fountain takes the shape of a half sphere with diameter 10 feet that sits, flat side down, in the center of a round brick-paved patio of diameter 100 feet. What is the area of the portion of the patio that is left uncovered?

Answer 1

1. Check the picture below. It illustrates an upper view of the fountain, which forms a circle with radius 5 ft, and the patio, with radius equal to 50 ft.

2. Area(fountain)=Area(Circle with radius 5)=$\pi * 5^{2}=25 \pi$ (ft squared)

Area(patio)= Area(Circle with radius 50)=$\pi * 50^{2}=2500 \pi$ (ft squared)

3. Area (uncovered) = Area(patio)-Area(fountain)=$2500 \pi-25 \pi=2475 \pi$(ft squared)

Answer: $2475 \pi$ ft squared