Question

The volume of a box(v) varies directly with its length(l). If one of the boxes has a volume of 288 cubic inches and a length of 12 inches, what is the constant of proportionality for the group of boxes?

1) 1/24
2) 3,456
3) 24

Answer 1

The constant of proportionality for the group of boxes is 24.

Step-by-step explanation:

The volume of a box varies directly with its length. This means that if the length increases, the volume also increases, and vice versa. The direct variation equation for this relationship is given by v = kl, where v is the volume, k is the constant of proportionality, and l is the length.Using the given information, we have a box with a volume of 288 cubic inches and a length of 12 inches. Substituting these values into the direct variation equation, we get 288 = 12k. To solve for k, we divide both sides of the equation by 12: k = 24.Therefore, the constant of proportionality for the group of boxes is 24.