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

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Physics

1 August, 08:14

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

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Alijah Mckee · Answer 1

1000

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.