Question

box a has a volume of 216 cubic meters. box b is similar to box a. to create box b, box as dimensions were divided by 2. what is the volume of box b? 27 m³ 72 m³ 108 m³ 54 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 \(k=\frac{1}{2}\) (since Box B's dimensions are obtained by dividing Box A's dimensions by 2).

Step2: Calculate the volume of Box B

Let \(V_A = 216\space m^{3}\) be the volume of Box A. Using the formula \(V_B=V_A\times k^{3}\), substitute \(k = \frac{1}{2}\) into the formula. So \(V_B=216\times(\frac{1}{2})^{3}\).
First, calculate \((\frac{1}{2})^{3}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}\).
Then, \(V_B = 216\times\frac{1}{8}\).
Since \(216\div8 = 27\).

Answer:

\(27\space m^{3}\)