M is directly proportional to r cubed when r = 4, m = 160. Find the value of r when m = 540
       
      
                
     
    
    
    
    
    1 answer:
            
              
              
                
                
Answer:
r = 6
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportionality
To find k use the condition r = 4 when M = 160
k =  =
 =  = 2.5, so
 = 2.5, so
M = 2.5r³ ← equation of proportionality
When M = 540, then
540 = 2.5 r³ ( divide both sides by 2.5 )
216 = r³ ( take the cube root of both sides )
r = ![\sqrt[3]{216}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216%7D) = 6
 = 6
 
                                
             
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