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

Sagot :

absor201

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

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