Leftover Cookie

Geometry Level 1

Cookie Monster has a large circle of cookie dough.
He cuts out 7 small cookies, as shown in the diagram above.
He then gathers up all the leftover parts and reshapes them.

How many more cookies (of the same size) can he make?

1 0 2 3

1 solution

Peter van der Linden
Nov 11, 2016

Let's say the big circle has radius R. The radius of a small circle then is R/3. So the area of a small circle is $1/9*R^2$ . Since there are 7 cookies the leftovers have area $2/9*R^2$ . Which means 2 cookies

Like this problem! However, I guess the composer should clarify that the new cookies are also equal to the previous 7 ones.

William Nathanael Supriadi - 4 years, 7 months ago

I have resolved using a slightly different approach, not 100% mathematically.

Let's assume that the bug circle has a diameter of D. The diameter of the smallest circles are D/3. The radius is half of the diameter.

We know that the area of the big circle is πr^2. The area of the small circles is π(r/3)^2. If we divide these areas, we will know how many circles we can have.

To make it simple I gave values to the variables. Let's say r=9. So (π9^2)/(π3^2) => simplify π and 3^2 we have 9 circles. If we subtract the 7 we already have we can make 2 more circles with the left overs.

Paco Fernández Rodríguez - 4 years, 7 months ago

.04 short of 2 cookies Correct answer is 1 cookie

Paul Portman - 4 years, 7 months ago

Why 0.04 short?

Peter van der Linden - 4 years, 7 months ago

You didn't say that he gathers the left part again and again until the shape is smaller than a cookie. So I think the answer is 1;)

shithil Islam - 4 years, 6 months ago

Leftover Cookie

1 solution

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