Question

M is proportional to the cube of r. when r=3m,m=216.when r=5 find the value of m

Answer 1

The value of m is 1000 for r=5

Explanation:

Given that m is proportional to the cube of r

It can be written as:

`m \propto\ r^3`

When the proportionality symbol is removed a proportionality constant is introduced in the equation.

Let k be the proportionality constant

`m = kr^3`

Given

r=3,m=216

Putting the values

`216 = k(3)^3\\216 = k * 27\\k = (216)/(27)\\k = 8`

The equation will now become

`m = 8r^3`

Putting r = 5

`m = 8(5)^3\\m = 8 * 125\\m = 1000`

Hence,

The value of m is 1000 for r=5