Answer:
r = 8
Step-by-step explanation:
Given that M is directly proportional to r² then the equation relating them is
M = kr² ← k is the constant of proportionality
To find k use the condition when r = 2 , M = 14
k = [tex]\frac{M}{r^{2} }[/tex] = [tex]\frac{14}{4}[/tex] = [tex]\frac{7}{2}[/tex]
M = [tex]\frac{7}{2}[/tex]r² ← equation of proportion
When M = 224, then
224 = [tex]\frac{7}{2}[/tex]r² ← multiply both sides by 2
7r² = 448 ( divide both sides by 7 )
r² = 64 ( take the square root of both sides )
r = [tex]\sqrt{64}[/tex] = 8
