Question

The volume of a ball, V cm", is directly proportional to the cube of its radius, r. When r = 7.5. V = 562.54 cm (a) Find the equation connecting V and r. Give the value of k, the constant, in terms of . (b) Calculate the value of V when r = 9, giving your answer in terms of .​

Answer 1

`v = k {r}^(3)`

`562.54 = k * {7.5}^(3)`

`562.54 = 421.88k`

`k = 562.54 / 421.88`

`k = 1.33`

since

`v = k {r}^(3)`

`v = 1.33 * {9}^(3)`

`v = 729 * 1.33`

`v = 969.57`