Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B?
A. 864 m^3
B. 288 m^3
C. 96 m^3
D. 32 m^3
Answer (2)
The volume of Box A is given as 32 m 3 .
The dimensions of Box B are three times the dimensions of Box A.
The volume of Box B is 3 3 = 27 times the volume of Box A.
Calculate the volume of Box B: V B = 27 × 32 = 864 m 3 . The volume of Box B is 864 m 3 .
Explanation
Define volumes Let V A be the volume of Box A and V B be the volume of Box B. We are given that V A = 32 cubic meters.
Calculate the scaling factor Since Box B is similar to Box A and its dimensions were tripled, the volume of Box B is 3 3 = 27 times the volume of Box A.
Calculate the volume of Box B Therefore, V B = 27 × V A = 27 × 32 = 864 cubic meters.
State the final answer The volume of Box B is 864 cubic meters.
Examples
Imagine you're designing a storage container, and you want to create a larger version that maintains the same proportions as a smaller one. If you triple the dimensions of the original container, the new container will have 27 times the volume of the original. This principle applies to various real-world scenarios, from scaling up architectural models to understanding how changes in size affect the capacity of tanks or containers.
The volume of Box B, created by tripling the dimensions of Box A, is 864 cubic meters. This is calculated by recognizing that the volume increases by a factor of 27 when dimensions are tripled. Therefore, the answer is A .864 m 3 .
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