The square surface cover shown in the figure is 10.16 centimeters on each side. The knockout in the center of the cover has a diameter of 1.27 centimeters. Find the area of the cover to the nearest hundredth centimeter.

asked 2020-11-08
The square surface cover shown in the figure is 10.16 centimeters on each side. The knockout in the center of the cover has a diameter of 1.27 centimeters. Find the area of the cover to the nearest hundredth centimeter.

Answers (1)

The area of the cover is the area of the square minus the area of the circle: Acover=Asquare-Acircle Acover=\(\displaystyle{8}^{{2}}-\frac{{π{d}^{{2}}}}{{4}}\)
Substitute s=10.16 cm and d=1.27 cm: Acover=\(\displaystyle{10.16}^{{2}}-{\left(π\frac{{\left({1.27}\right)}^{{2}}}{{4}}\right.}\)
Use a calculator and round to the nearest hundredth cm (2 decimal places):
Acover≈101.96 cm

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