Question

The volume, V, of a container is directly proportional to the cube of its height, h. When its height

is 4 cm, its volume is 48 cm3.
1.What is the volume if the height is 3 cm?
2.If the height is doubled to 6 cm, how many times bigger will the volume be?

Answer 1

see explanation

Explanation:

given that V is directly proportional to h³ , then the equation relating them is

V = kh³ ← k is the constant of proportion

to find k use the condition V = 48 when h = 4 , then

48 = k × 4³ = 64k ( divide both sides by 64 )

`(48)/(64)` = k , then k = 0.75

V = 0.75h³ ← equation of proportion

1

when h = 3 , then

V = 0.75 × 3³ = 0.75 × 27 = 20.25 cm³

2

when h = 6 , then

V = 0.75 × 6³ = 0.75 × 216 = 162 cm³

then

162 ÷ 20.25 = 8

the volume will be 8 times bigger