You are designing a dome house in the shape of a hemisphere with a 31 ft outside diameter. Two coats of sealer are required to cover and seal the exposed external concrete. If one gallon covers 110 ft ², how many gallons are required for the bill of materials? A) 27 gallons B) 54 gallons C) 20 gallons D) 30 gallons E) 40 gallons

Question

Quizplus · Accepted Answer

The surface area of a hemisphere is given by $2\pi r^2$, where $r$ is the radius. The radius here is half the diameter, so $r = 31/2 = 15.5$ ft. Thus, the surface area is $2\pi (15.5)^2 \approx 1507.96$ square feet. Since one gallon covers 110 square feet, for one coat, you'd need $1507.96 / 110 \approx 13.71$ gallons. Since two coats are required, you'd need approximately $13.71 \times 2 = 27.42$ gallons. Rounding to the nearest whole number gives 27 gallons.

You Are Designing a Dome House in the Shape of a Hemisphere