Question

Kevin goes to the grocery store and buys a box of cereal, a family size box of cereal, a candy bar, and a king sized candy bar. He notices that the family sized box of cereal is twice as big as the regular box of cereal and the king size candy bar is twice as big as the regular candy bar. Kevin believes that because the family sized box of cereal and king sized candy bar are twice the size that the volume is also twice the size. Is Kevin correct in his thinking?

Answer 1

Kevin is partially correct. Just because an object is larger in one dimension does not mean its volume is directly proportional to that increase.

Step-by-step explanation:

Kevin is partially correct in his thinking. While the family sized box of cereal and king sized candy bar are twice the size of the regular box of cereal and candy bar, their volumes are not necessarily twice the size.

Volume is determined by the three-dimensional space an object occupies. Just because an object is larger in one dimension (length, width, or height) does not mean its volume is directly proportional to that increase. To calculate volume, you need to consider all three dimensions. In this case, multiplying only one dimension by 2 is not sufficient to determine the change in volume.

To illustrate this, imagine two cubes. One cube has sides measuring 2 cm, while the other cube has sides measuring 4 cm. Even though the second cube's sides are twice as long as the first cube's sides, its volume is eight times larger because every dimension has been multiplied by 2 (2 x 2 x 2).

Answer 2

Yes, he is thinking correctly.