Box A has a volume of 512 cubic meters. Box B is similar to box A. To create Box B, Box A's dimensions were divided by 2. What is the volume of Box B?Group of answer choices256 m3170 m3128 m364 m3
Question
Box A has a volume of 512 cubic meters. Box B is similar to box A. To create Box B, Box A's dimensions were divided by 2. What is the volume of Box B?Group of answer choices256 m3170 m3128 m364 m3
Solution
The volume of a box (or any three-dimensional object) is calculated by multiplying its length, width, and height. If Box B is similar to Box A, it means that the proportions between the corresponding sides are the same.
In this case, all dimensions of Box B are half of those of Box A. So, if we let L, W, and H represent the length, width, and height of Box A, then the volume of Box A is LWH = 512 cubic meters.
The dimensions of Box B are L/2, W/2, and H/2. Therefore, the volume of Box B is (L/2)(W/2)(H/2) = LWH/8.
Since the volume of Box A is 512 cubic meters, the volume of Box B is 512/8 = 64 cubic meters.
So, the volume of Box B is 64 m^3.
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