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| Math Central | Quandaries & Queries |
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Question from Jone, a student: If a hemispheric dome has a height of 20m and it take 5 gallons of paint to paint the floor, how many gallons of pain are needed to paint the inside of the dome? |
Hi Jone,
If the dome is a hemisphere and its height is 20 m then the radius of the dome is 20 m. The floor is then a circular disk of radius 20 m. What is the areas of the floor in meters squared? It takes 5 gallons of paint to paint the floor so divide 5 gallons by the area of the floor to find the coverage of the paint in gallons per square meter.
The surface area of a sphere is 4 π r2, where r is the radius and hence the surface area of a hemisphere is half this quantity. What is the surface area of a hemisphere of radius 20 meters? You know the coverage of the paint is gallons per square meter so how many gallons will it take to paint the hemisphere?
Penny
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