Question

question 9(multiple choice worth 1 points)
(06 02 mc)
box a has a volume of 48 cubic meters. box b is similar to box a. to create box b, box as dimensions were doubled. what is the volume of box b?
o 24 m³
o 96 m³
o 144 m³
o 384 m³

Explanation:

Step1: Recall the volume formula for similar solids

If two solids are similar and the scale factor of their corresponding linear dimensions is \(k\), the ratio of their volumes is \(k^{3}\). Here, the scale factor \(k = 2\) (since Box B's dimensions are double Box A's).

Step2: Calculate the volume of Box B

Let \(V_A=48\space m^{3}\) be the volume of Box A. Using the formula \(V_B=V_A\times k^{3}\), substitute \(k = 2\) into the formula. So \(V_B=48\times2^{3}\).

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Answer:

\(384\space m^{3}\)