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:

Answer:

First, find the area of the paper: \( 6 \times 10 = 60 \) square inches.
Then, find the radius of each circle. From the diagram, the height of the paper is 6 inches with 3 rows of circles, so the diameter of each circle is \( 6 \div 3 = 2 \) inches, so radius \( r = 1 \) inch.
Area of one circle: \( \pi r^2 = \pi(1)^2 = \pi \) square inches.
Area of 15 circles: \( 15\pi \) square inches.
Wasted paper area = Area of paper - Area of 15 circles = \( 60 - 15\pi \) square inches.

So the answer is \( (60 - 15\pi) \) square inches (the first option).