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

Answer:

1) When r = 2, M = 20.

2) When M  = 540, r = 6.

Step-by-step 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

$M = ar^3$

$160 = a(4^3)$

$64a = 160$

$a = \frac{160}{64}$

$a = 2.5$

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

$M = 2.5r^3$

$540 = 2.5r^3$

$r^3 = \frac{540}{2.5}$

$r^3 = 216$

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

$r = 6$

When M  = 540, r = 6.