Question

M is directly proportional to r^3 , when r=4 and m=160 , work out the value when m=540

Answer 1

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hi

Answer 2

The value of r is 6

Step-by-step explanation:

1. Here it is given that M is directly proportional to $\mathbf{r^{3}}$. So this is case of direct proportion.

2. We can write in this way

 

   $\mathbf{\frac{M_{2}}{M_{1}}=\frac{r_{2}^{3}}{r_{1}^{3}}}$

   or

   $\mathbf{\frac{M_{2}}{M_{1}}=\left ( \frac{r_{2}}{r_{1}} \right )^{3}}$        ...1)

3. Where in equation 1)

   $\mathbf{M_{1}=160}$

   $\mathbf{M_{2}=540}$

   $\mathbf{r_{1}=4}$

4. Again from equation 1), on putting respective value

   $\mathbf{\frac{540}{160}=\left ( \frac{r_{2}}{4} \right )^{3}}$

   on solving L.H.S of above equation

   $\mathbf{\frac{27}{8}=\left ( \frac{r_{2}}{4} \right )^{3}}$           ...2)

5. L.H.S of equation 2) can be written as

   $\mathbf{\left ( \frac{3}{2} \right )^{3}=\left ( \frac{r_{2}}{4} \right )^{3}}$

  So

   $\mathbf{\frac{3}{2}=\frac{r_{2}}{4}}$

  So

  $\mathbf{r_{2}=\frac{4\times 3}{2}=6}$

6. You can find other example like this

    https://brainly.in/question/8160898