Question

If a length and diameter of a pencil are both multiplied by 10, then the volume is multiplied by ?

Answer 1

1000

Step-by-step explanation:

If we model the pencil as a cylinder:

V = π r² h

Or, in terms of diameter:

V = π/4 d² h

If we multiply d and h by 10:

V = π/4 (10 d)² (10 h)

V = 1000 (π/4 d² h)

The volume increases by a factor of 1000.