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?
+37103 For ease, let's make it a 10" diameter pizza.
so the square has a diagonal of 10"
using pythagorean theorem we can find the sides of the triangle formed by the diagonal through the square
10^2 = 2 (side^2) (since each side is the same length)
100/2 = side^2
50 = side^2
7.07 = side length
so the square has an area of 7.07 x 7.07 = 50 sq inches
the total area of the ROUND pizza is pi x r^2= 3.14 x (5^2) = 78.54 sq inches
How much is left after taking out the square? 78.54-50 = 28.54 sq inches remaining.
Question asks what per centage remains
28.54/78.54 x 100% = 36% remains.
