M is directly proportional to r3

When r = 4, M = 160

a) Work out the value of M when r = 2.

M = 20

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 proportion

To find k use the condition when r = 4, M = 160, that is

160 = k * 4³ = 64k (divide both sides by 64)

2.5 = k

M = 2.5r³ ← equation of proportion

When r = 2, then

M = 2.5 * 2³ = 2.5 * 8 = 20

Mr³

M=kr³ (k = constant)

when M=160, r=4

160=k (4) ³

160=64k

k=2.5

therefore, M=2.5r³

when r=2

M=2.5r³

M=2.5 (2) ³

M=2.5 (8)

M=20