Question

C is directly proportional to the cube of D When D = 5, C = 175 (a) Work out the value of C when D = 6 (b) Work out the value of D when C = 4725​

Answer 1

(a) C = 302.4 (b) D = 15

Explanation:

given C is directly proportional to D³ then the equation relating them is

C = kD³ ← k is the constant of proportionality

to find k use the condition when D = 5, C = 175 , then by substitution

175 = k × 5³ = 125k ( divide both sides by 125 )

1.4 = k

C = 1.4D³ ← equation of proportion

(a)

when D = 6 , then substituting into the equation gives

C = 1.4 × 6³ = 1.4 × 216 = 302.4

(b)

when C = 4725 , then substituting into the equation gives

4725 = 1.4D³ ( divide both sides by 1.4 )

3375 = D³ ( take cube root of both sides )

`\sqrt[3]{3375}` =
`\sqrt[3]{D^3}` , that is

D = 15