Question

M is a directly proportional to r cubed when r=4 M=160

1) work out the value of M when r=2
2) work out the value of r when M=540

Answer 1

1) When r = 2, M = 20.

2) When M = 540, r = 6.

Explanation:

M is a directly proportional to r cubed

This means that the equation for M has the following format:

`M = ar^3`

In which a is a multiplier.

When r=4 M=160.

We use this to find a. So

`M = ar^3`

`160 = a(4^3)`

`64a = 160`

`a = (160)/(64)`

`a = 2.5`

So

`M = 2.5r^3`

1) work out the value of M when r=2

`M = 2.5*2^3 = 2.5*8 = 20`

When r = 2, M = 20.

2) work out the value of r when M=540

`M = 2.5r^3`

`540 = 2.5r^3`

`r^3 = (540)/(2.5)`

`r^3 = 216`

`r = \sqrt[3]{216}`

`r = 6`

When M = 540, r = 6.