Question

the amount of juice in a grapefruit is directly proportional to the cube of the cube of its diameter. let j represent the amount of juice (in fluid ounces) in a grapefruit let d represent the diameter (in inches) of the grapefruit and let k be the constant of proportionality. write an equation that relates j to d. j= ______a grapefruit with a 4 in diameter contains 6 fluid ounces of juice. use the equation that relates j to d and the known info to find k. k=______how many fluid ounces of juice is contained in a grapefruit with a 5 in diameter? round to the nearest tenth of a fluid ounce.

Answer 1

First, find the constant of proportionality.

`j=k\cdot d^3`

Where d = 4 in and j = 6 oz. Solve for k.

`\begin{gathered} k=(j)/(d^3)=(6oz)/((4in)^3)=(6oz)/(64in^3) \\ k=0.09375\cdot(oz)/(in^3) \end{gathered}`

Then, use the constant of proportionality to find the number of fluid ounces for 5 inches pf diameter.

`\begin{gathered} j=0.09375\cdot(oz)/(in^3)\cdot(6in)^3 \\ j=0.09375\cdot(oz)/(in^3)\cdot216in^3 \\ j=20.25oz \end{gathered}`

Therefore, the number of fluid ounces of juice contained in a grapefruit with a 5 inches diameter is 20.25 oz.