Why multiplying 37.4 * 0.01 gives a product that is less than 37.4?

You are essentially finding one hundredth of 37.4. In other words, what number multiplied by 100 gives you 37.4? The answer being 0.374 shows the the product is less than 37.4.

Draw a diagram to illustrate the problem as shown below.

Calculate the volume of the empty cone.
V₁ = (1/3)π*(6 in)²*(10 in) = 120π in³

Calculate the volume of the sphere.
V₂ = (4/3)π*(1.5 in)³ = 4.5π in³

The volume that can be filled with flavored ice is 
V = V₁ - V₂ = 115.5π in³ = 362.85 in³

Th volume is 115.5π in³ or 362.9 in³ (nearest tenth)