Question

Rectangular prism A with volume 96m³

Rectangular prism B with volume 12m³

Rectangular prism A is similar to rectangular prism B, where the longest side of rectangular prism A corresponds to the longest side of rectangular prism B. The table gives the volumes, in cubic meters (m³), of the two prisms. The length of the longest side of rectangular prism A is 6 meters. What is the length, in meters, of the longest side of rectangular prism B?

Answer 1

The length of the longest side of rectangular prism B is 3 meters, calculated by dividing the longest side of similar rectangular prism A by the scale factor derived from the cube root of the ratio of their volumes.

Step-by-step explanation:

To solve for the length of the longest side of rectangular prism B, we'll need to understand the relationship between similar figures and how their volumes are related. In this case, rectangular prism A is similar to rectangular prism B and has a volume that is 8 times larger (96m³ for A compared to 12m³ for B). Since similar figures have sides in the same ratio, and volume scales with the cube of the side length ratio, we can set up a proportion to find the corresponding side length for B.

The volume of a shape increases with the cube of the linear dimensions, so if we know that the longest side of A is 6 meters, we can find the scale factor by taking the cube root of the volume ratio:

• Scale factor = ∛(Volume of A / Volume of B) = ∛(96/12) = 2

Now, we just divide the known longest side of A by this scale factor to get the longest side of B:

• Longest side of B = Longest side of A / Scale factor = 6m / 2 = 3m

So, the length of the longest side of rectangular prism B is 3 meters.