Ms Happy has decided to start wearing a face mask, because it is now required of her to do so. The mask she has started wearing is very colorful and measures 9 inches by 5 inches. She is extremely bored, so she wonders what percent of her face is uncovered. Given that her face is roughly the shape of a circle (she put on a few pounds over Spring Break and Easter) with a circumference of 30 inches, find the percent of her face that is uncovered. Use 3.14 for pi and round your answer to 2 decimal places and don't forget the percent symbol.

Question

Mathematics

Amir Romero

2 May, 13:19

Ms Happy has decided to start wearing a face mask, because it is now required of her to do so. The mask she has started wearing is very colorful and measures 9 inches by 5 inches. She is extremely bored, so she wonders what percent of her face is uncovered. Given that her face is roughly the shape of a circle (she put on a few pounds over Spring Break and Easter) with a circumference of 30 inches, find the percent of her face that is uncovered. Use 3.14 for pi and round your answer to 2 decimal places and don't forget the percent symbol.

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Answers (1)

Know the Answer?

Iliana Burch · Answer 1

37.20 %

Step-by-step explanation:

Circumference = 2 * pi * r

30 = 2 * 3.14 * r

r = 4.7770700637

Area of her face = pi * r²

3.14 * 4.7770700637²

= 71.6560509556 in²

Area of the mask = 9 * 5 = 45 in²

Uncovered area

= 71.6560509556 - 45

= 26.6560509556 units²

% of uncovered area:

26.6560509556/71.6560509556 * 100

37.2%