Volume of a right circular cylinder Find the volume (in cm³) of a right circular cylinder with diameter 21 cm and height 10 cm.

Introduction / Context:The volume of a cylinder is V = π r^2 h. With a given diameter, we first halve it to get the radius, square it, and multiply by height and π.

Given Data / Assumptions:

• Diameter = 21 cm ⇒ radius r = 10.5 cm
• Height h = 10 cm
• Use π = 22/7 for an exact integer outcome.

Concept / Approach:Compute r^2, then apply V = π r^2 h. Keeping π as 22/7 simplifies to an exact value when r is a half-integer compatible with 7.

Step-by-Step Solution:

Verification / Alternative check:Using π ≈ 3.14 yields ≈ 3462 cm³, which rounds to the exact 3465 obtained with 22/7—options list the exact value.

Why Other Options Are Wrong:3118, 3275, 3621 do not match π r^2 h with r = 10.5 and h = 10; only 3465 does.

Common Pitfalls:Using diameter in place of radius (forgetting to halve) or squaring 21 instead of 10.5 leads to large errors.

Final Answer:3465