Volume of iron in a hollow roller: A hollow cylindrical garden roller is 63 cm long with girth (outer circumference) 440 cm. Iron thickness is 4 cm. Find the volume of iron used (in cubic cm). Take π = 22/7.

Introduction / Context:For a hollow cylinder, volume of material equals π (R^2 − r^2) L. The girth gives the outer radius. Subtracting thickness yields the inner radius. Substitute and compute with π = 22/7.

Given Data / Assumptions:

• Length L = 63 cm
• Outer circumference C = 440 cm ⇒ R = C / (2π)
• Thickness t = 4 cm ⇒ inner radius r = R − 4
• π = 22/7

Concept / Approach:

• Compute R, r, then V = π (R^2 − r^2) L = π (R − r)(R + r)L.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 54982 / 57636 cm3: Arithmetic slips.
• 56372 cubic m: Wrong unit (m vs cm).

Common Pitfalls:

• Using diameter instead of radius after circumference.
• Forgetting to subtract thickness from the radius (not diameter).

Final Answer:

107712 cubic cm