Question

for a class project, a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches. how much paper is wasted? (60 - 15π) square inches; 15π square inches; 45 square inches; (60 - π) square inches

Explanation:

Step1: Calculate area of paper

The paper is a rectangle with length $l = 10$ inches and width $w=6$ inches. The area of a rectangle $A_{paper}=l\times w$. So, $A_{paper}=10\times6 = 60$ square - inches.

Step2: Calculate area of one circle

From the right - triangle in the upper - right corner of the figure, we can see that the radius of each circle $r = 1$ inch. The area of a single circle is given by the formula $A_{circle}=\pi r^{2}$. So, $A_{circle}=\pi\times1^{2}=\pi$ square inches.

Step3: Calculate area of 15 circles

Since there are 15 congruent circles, the total area of the 15 circles $A_{circles}=15\times A_{circle}=15\pi$ square inches.

Step4: Calculate wasted area

The wasted area $A_{wasted}=A_{paper}-A_{circles}$. So, $A_{wasted}=60 - 15\pi$ square inches.

Answer:

$(60 - 15\pi)$ square inches