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 = [tex]\frac{M}{r^3}[/tex] = [tex]\frac{160}{64}[/tex] = 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 = [tex]\sqrt[3]{216}[/tex] = 6
