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