If a baking sheet holds 12 cookies and each has a diameter of 3 in. what is the area of the unused part?

Question

If a baking sheet holds 12 cookies and each has a diameter of 3 in. what is the area of the unused part?

Answer 1

Area covered by one cookie = pi(r²)

12 cookies = 12(3.14)1.5² = 84.78 in².

If you lay out the cookies in four rows of three each,

that requires the sheet area of 9 by 12 inches

or 108 in².

Providing you assume placing the cookies on the edges of the baking sheet and touching each other

108 - 84.78 = 23.22 in² is the unused part of the sheet.

Answer 2

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let's pretend those are cookies and they are touching. the area of the baking sheet would be 12x9 = 108sqinches. we don't have to know the dimensions of the sheet. as long as we know that it hold 12 cookies, the dimensions could be 3 by4 or 1 by 12 or 2by6. the area is still the same.

now, the area of the cookies are pi*r^2. r=3/2

so each cookie are = pi(3/2)^2 = 9/4 pi

multiply that by 12 cookies:

(12)9/4 pi = 27pi square inches

so the sheet is 108 square inches. and the cookies are only taking up 27pi square inches.

108 - 27pi = unused part

108 - 84.823 = unused part

23.177 square inches is the unused part.