   SEARCH HOME Math Central Quandaries & Queries  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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.