Question

M is directly proportional to r3

When r = 4, M = 160
a) Work out the value of M when r = 2.​

Answer 1

M<varies>r³

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

Answer 2

M = 20

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