M is directly proportional to r^3 When r = 4, M= 160
b) work out the value of r when m = 540

r=6

Step-by-step explanation:

Proportions

We know M is directly proportional to

This can be written as

Where k is the constant of proportionality which will be determined knowing that when r = 4, M= 160. Substituting in the equation above:

Solving for k:

The equation is:

Now find r when M=540:

Dividing by 2.5:

Taking cube roots:

r=6

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