SOLUTION: An oil company distributes oil in a metal can shaped like a cylinder that has an actual radius of 5.1 cm and a height of 15.1 cm. A worker incorrectly measured the radius as 5 cm a

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Question 752527: An oil company distributes oil in a metal can shaped like a cylinder that has an actual radius of 5.1 cm and a height of 15.1 cm. A worker incorrectly measured the radius as 5 cm and the height of 15 cm. Determine the relative error in calculating the surface area, to the nearest thousandth.
Answer by Theo(13342) About Me  (Show Source):
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surface area equals two times the area of the base plus the lateral area.

area of the base = pi * r^2

lateral area = 2 * pi * r * h

total surface area = 2 * pi * r^2 + 2 * pi * r * h

desired measurements are radius of 5.1cm and height of 15.1 cm.

surface area with those measurements = 2 * pi * (5.1)^2 + 2 * pi * 5.1 * 15.1

this is equal to 647.2937503 square cm.

actual measurements are radius of 5 cm and height of 15 cm.

surface area with those measurements = 2 * pi * 5^2 + 2 * pi * 5 * 15

this is equal to 628.3185307

the difference from the desired amount is equal to 18.97521963 square cm.

the % difference from the desired amount is equal to 3.02%