Question

M is directly proportional to r cubed when r = 4, m = 160. Find the value of r when m = 540

Answer 1

r = 6

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 =
`(M)/(r^3)` =
`(160)/(64)` = 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}` = 6