Digital SAT Math Practice Question #1174
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What are the individual geometric shapes that make up the exterior surface to be painted? Remember to exclude any surfaces that are on the ground or covered by another part of the silo.
Recall the formulas for the lateral surface area of a cylinder and the curved surface area of a hemisphere. Be careful not to include the flat base of the hemisphere or the circular base of the cylinder that is on the ground.
Quickly identify the two components needing paint: the cylinder's side and the hemisphere's dome. Recall their formulas: \(2\pi rh\) for the cylinder's lateral surface and \(2\pi r^2\) for the hemisphere's curved surface. Substitute the given values \(r=10\) and \(h=30\): \(2\pi(10)(30) = 600\pi\) and \(2\pi(10)^2 = 200\pi\). Sum these two values: \(600\pi + 200\pi = 800\pi\). Scan the options for \(800\pi\). This direct calculation is efficient and less prone to error than trying to eliminate options without calculation.
To find the total exterior surface area that will be painted, we need to calculate the sum of the lateral surface area of the cylindrical part and the curved surface area of the hemispherical top. The base of the silo rests on the ground an...
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