You are given a sheet of cardboard that is 8.0 in. x 11.0 in. how many full circles with a diameter of 3.0 inches can you cut from the cardboard? what is the percentage of waste if the excess cardboard (outside the circles) is thrown away?

Question

Mathematics

Isabel

10 April, 08:34

You are given a sheet of cardboard that is 8.0 in. x 11.0 in. how many full circles with a diameter of 3.0 inches can you cut from the cardboard? what is the percentage of waste if the excess cardboard (outside the circles) is thrown away?

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Answers (1)

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Caleb Baxter · Answer 1

The answer is there are eight circles that can be cut from an 8.0 x 11.0 in sheet but nine circles won’t fit.

Area of 8 circles is pir^2 = 8pi (1.5) ^2 = 56.55 in^2

Total area of the cardboard = (8.0 in) (11.0 in) = 88.0 in^2

Area of waste = 88 in ^2 - 56.55 in^2 = 31.35 in^2

Percent of waste = 31.35 in^2 / 88.0 in^2 x 100% = 37.5% is the answer.