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There are 900 toothpicks in a​ regular-sized box. If a jumbo box is made by tripling all the dimensions of the​ regular-sized box, how many toothpicks will the jumbo box​ hold?

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AL2006

When you triple the height of the box, it can hold (900 x 3) = 2,700 pieces.

Then triple its length, and it can hold (2,700 x 3) = 8,100 pieces.

Then triple its width, and it can hold (8,100 x 3) = 24,300 pieces.

When you triple the dimensions of a 3D object, it has 27 times its original volume.  (900 x 27) = 24,300 .

facundo3141592

Answer: 24300 toothpicks

Step-by-step explanation:

The volume of the box can be written as:

V0 = W*L*H

where W is the width, L is the length and H is the height.

We know that in V0 we can put 900 toothpicks.

Now, if we triply each of the dimensions we have that:

V = 3W*3L*3H = (3*3*3)*W*L*H

and we know that W*L*H = V0

V = 27*V0

and if in V0 we can put 900 toothpicks, then in V we can put 27 times that amount, this is:

27*900 = 24300 toothpicks

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