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Summer Clouds moderators

24/11/2017 at 13:54
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Paige cuts a square out of a circular pizza. The corners of the square lie on the circumference of the pizza. To the nearest whole number, what percent of the pizza is left when Paige removes the square? 




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    Phan Thanh Tinh Coordinator 24/11/2017 at 18:17

    Let r be the radius of the pizza, then the length of the edge of the square is \(\sqrt{2}r\)

    The area of the square is : \(\left(\sqrt{2}r\right)^2=2r^2\)

    The area of the pizza is : \(r^2\pi\)

    The area of the remaining pizza is : \(r^2\pi-2r^2=r^2\left(\pi-2\right)\)

    The answer is : \(\dfrac{r^2\left(\pi-2\right).100}{r^2\pi}\%=100\left(1-\dfrac{2}{\pi}\right)\%\approx36\%\)

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    Nguyễn Hiền 29/11/2017 at 08:47

    Please rendering a pizza of the pizza, then the length of the right of wide's square is   √ 2 r2r

    Dừng của hình vuông là:   ( √ 2 r ) 2 = 2 r 2(2r)2=2r2

    Khu vực pizza là:   r 2 πr2π

    Khu vực của bánh pizza còn lại là:   r 2 π - 2 r 2 = r 2 ( π - 2 )r2π-2r2=r2(π-2)

    Câu trả lời là:   r 2 ( π - 2 ) .100 r 2 π% = 100 ( 1 - 2 π) % ≈ 36 %


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