Question

Help me please...............

Answer 1

a)
`M = 20`

b)
`r=6`

Explanation:

a)

Given that

`M` ∝
`r^3`

Say

`M=kr^3` --------------(A)

Where is k is constant of proportionality

We are also given that

When r = 4 , M = 160

Hence

`160 = k * 4^3`

`160=k * 64`

`k = (160)/(64)`

`k = (5)/(2)`

Now we are asked to determine

a) M when r = 2

Putting the values of k and r in equation (A)

`M= (5)/(2) * 2^3`

`M= (5)/(2) * 8`

`M= (5 * 8)/(2)`

`M= 5 * 4`

`M = 20`

b) r , when M = 540

Putting the value of M and k in equation A again

`540 = (5)/(2) * r^3`

`r^3=540 * (2)/(5)`

`r^3 = (2 * 540)/(5)`

`r^3 = 2 * 108`

`r^3=216`

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

`r=6`