SOLUTION: a rectangular acrylic sheet is 36 cm by 25cm. from it, 56 circular buttons.each of diameter 3.5 cm have been cut out. find the area of remaining sheet.

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Question 935636: a rectangular acrylic sheet is 36 cm by 25cm. from it, 56 circular buttons.each of diameter 3.5 cm have been cut out. find the area of remaining sheet.
Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if a rectangular acrylic sheet is 36cm by 25cm, then its area is
A=36cm%2A25cm
A=900cm%5E2
if 56 circular buttons, each of diameter d=3.5cm have been cut out, then radius is d%2F2=3.5cm%2F2=1.75cm
and, the area of all buttons is A%5B1%5D=56%2A%281.75cm%29%5E2%2Api
A%5B1%5D=56%2A3.0625cm%5E2%2A3.14
A%5B1%5D=538.51cm%5E2
the area of remaining sheet is
A-A%5B1%5D=900cm%5E2-538.51cm%5E2
A-A%5B1%5D=361.49cm%5E2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the sheet is:
+36%2A25+=+900+ cm2
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The radius of the buttons is:
+d%2F2+=+3.5%2F2+
+d%2F2+=+1.75+ cm
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The area of each button is:
+A+=+pi%2Ar%5E2+
+A+=+3.141%2A1.75%5E2+
+A+=+9.619+ cm2
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The total area of +56+ buttons is:
+56%2A9.619+=+538.682+ cm2
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The area left over is:
+900+-+538.682+=+361.319+ cm2