SOLUTION: If you make a cardboard box that is twice as wide, twice as tall, and twice as long as a cardboard box that you already have, how will the volume of the larger box compare with the

Question 998503: If you make a cardboard box that is twice as wide, twice as tall, and twice as long as a cardboard box that you already have, how will the volume of the larger box compare with the volume of the original box? (Will the larger box be twice as big, 3 times as big, 4 times as big, etc.?)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the volume will be 8 times as large.

let the dimensions of your original box be x,y,z

x is the width,
y is the height
z is the length.

the volume is therefore x * y * z

now you double each dimension, so the dimensions are now 2 * x, 2 * y, 2 * z.

the volume is therefore 2 * x * 2 * y * 2 * z = 8 * (x * y * z)

since the volume of the original box is equal to x * y * z, then:

the volume of the larger box is equal to 8 * the volume of the original box.

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