Question

How to find the volume of each shape of a roll of paper towels if its length = 11 width =9 and diameter =11

Answer 1

I need one quick clarification: do you mean the roll is a hollow cylinder with
- height (length) = 11,
- outer diameter = 11, and
- inner diameter (core) = 9 ?

If so, the volume of the paper (the cylindrical shell) is
V = π · h · (R^2 − r^2),
where R = outer radius = 11/2 = 5.5 and r = inner radius = 9/2 = 4.5.

Compute:
- R^2 = 5.5^2 = 30.25
- r^2 = 4.5^2 = 20.25
- R^2 − r^2 = 10

So V = π · 11 · 10 = 110π ≈ 345.6 cubic units (e.g., cubic inches if your dimensions are inches).

If instead you meant a solid cylinder (no hollow core) with diameter 11 and height 11, use
V = πr^2h = π·(5.5)^2·11 = 332.75π ≈ 1045.4 cubic units.

Tell me which interpretation is correct and what units you’re using if you want the answer adjusted.