Answer:
The value of m is 1000 for r=5
Step-by-step explanation:
Given that m is proportional to the cube of r
It can be written as:
[tex]m \propto\ r^3[/tex]
When the proportionality symbol is removed a proportionality constant is introduced in the equation.
Let k be the proportionality constant
[tex]m = kr^3[/tex]
Given
r=3,m=216
Putting the values
[tex]216 = k(3)^3\\216 = k * 27\\k = \frac{216}{27}\\k = 8[/tex]
The equation will now become
[tex]m = 8r^3[/tex]
Putting r = 5
[tex]m = 8(5)^3\\m = 8 * 125\\m = 1000[/tex]
Hence,
The value of m is 1000 for r=5
