Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?

Question

Ashtyn Spence

Mathematics

13 March, 12:22

Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?

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Jaylynn Grant · Answer 1

Okay, so if your rectangle is 16 by 8, that means that the circle diameter of 8 because that would be outside of the card's width,

the area of the rectangle is 16 x 8 or 128

the radius of the circle would be 4 (because 1/2 of the diameter is radius)

we know that the equation of the circle PIr^2, so the area of the circle is 16PI

then, the remaining area would be calculated by 128-16PI

This comes out to be approximately 77.73