Right circular cylinder – compute volume: Find the volume V of a right circular cylinder whose height (length) is 80 cm and whose base has diameter 14 cm (so radius = 7 cm). Give the answer in cubic centimeters.

Introduction / Context:This problem asks for the volume of a right circular cylinder from its basic dimensions. It reinforces correct identification of radius from diameter and direct substitution into the standard formula for cylindrical volume.

Given Data / Assumptions:

• Height h = 80 cm
• Diameter d = 14 cm → radius r = d/2 = 7 cm
• Use V = π * r^2 * h
• Use π ≈ 3.14 (or 22/7) for a numerical answer in cm^3

Concept / Approach:The volume of a right circular cylinder is proportional to both the cross-sectional area of the base (πr^2) and the height (h). After converting diameter to radius, compute r^2 and multiply by h and π.

Step-by-Step Solution:r = 14 / 2 = 7 cmr^2 = 49 cm^2V = π * 49 * 80 = 3920π cm^3Using π ≈ 3.14 → V ≈ 3920 * 3.14 ≈ 12308.8 cm^3 (rounds to about 12309–12320)Using π = 22/7 → V = 3920 * (22/7) = 560 * 22 = 12320 cm^3

Verification / Alternative check:Reverse check: 12320 / 80 = 154 cm^2, which equals π * 7^2 ≈ 153.94 cm^2 using π = 3.14. Consistency verified within rounding.

Why Other Options Are Wrong:1400 and 1553 cm^3 are too small by an order of magnitude; 13320 cm^3 overshoots the exact 22/7 result; 12000 cm^3 is an imprecise round number not matching π-based computation.

Common Pitfalls:Forgetting to halve the diameter to get radius; mixing units; dropping π inadvertently; arithmetic slips squaring 7 or multiplying by 80.

Final Answer:12320 cm^3