Question

A set of dolls is made so that the volume,V of each of them varies directly as the cube of its height h. The doll with a height of 3cm has a volume of 6.75 cm³.

A) find an equation for V in terms of H.
B) find the volume of a doll with a height of 2.5cm

Answer 1

V = 3.90625 cm³

Explanation:

Given that V varies directly as h³ then the equation relating them is

V = kh³ ← k is the constant of variation

To find k use the condition

V = 6.75 when h = 3 , then

6.75 = k × 3³ = 27k ( divide both sides by 27 )

0.25 = k

V = 0.25h³ ← equation of variation

(b)

When h = 2.5 , then

V = 0.25 × 2.5³ = 3.90625 cm³

Answer 2

A v=2.25 H=1

b. 5.625

Explanation: