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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?

Respuesta :

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)=[tex] \pi * 5^{2}=25 \pi [/tex] (ft squared)

Area(patio)= Area(Circle with radius 50)=[tex]\pi * 50^{2}=2500 \pi[/tex] (ft squared)

3. Area (uncovered) = Area(patio)-Area(fountain)=[tex]2500 \pi-25 \pi=2475 \pi [/tex](ft squared)

Answer: [tex]2475 \pi[/tex] ft squared
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