Assuming the shape of the balloon remains the same, the volume of the balloon is directly proportional to the cube of its height. Therefore, we can use the following proportion:
(air volume)₁ / (height)₁³ = (air volume)₂ / (height)₂³
where:
(air volume)₁ = 108 in.³ (when the height is 4 in.)
(height)₁ = 4 in.
(height)₂ = 8 in.
We can solve for (air volume)₂ as follows:
(air volume)₂ = (air volume)₁ × (height)₂³ / (height)₁³
(air volume)₂ = 108 in.³ × (8 in.)³ / (4 in.)³
(air volume)₂ = 108 in.³ × 64 / 64
(air volume)₂ = 108 in.³
Therefore, the balloon must hold 108 in.³ of air for the clown's face to be 8 in. tall.