Volume of a cone from radius and height: Find the volume of a cone with base radius 10 cm and height 21 cm. Express the answer approximately in cm^3.

Introduction / Context:The volume of a right circular cone is V = (1/3)πr^2h. Given r and h, this is a direct plug-in. Options are in approximate integers, so a decimal approximation with π works best here.

Given Data / Assumptions:

• r = 10 cm
• h = 21 cm
• V = (1/3)πr^2h

Concept / Approach:Compute r^2h first, then multiply by π/3. Using π ≈ 3.14 gives a tidy value near 2200 cm^3.

Step-by-Step Solution:r^2h = 10^2 * 21 = 100 * 21 = 2100V = (1/3)π * 2100 = 700π ≈ 700 * 3.14 ≈ 2198 cm^3Rounded to the nearest option → 2200 cm^3

Verification / Alternative check:Using π = 22/7 gives V = 700 * (22/7) = 2200 cm^3 exactly, confirming the choice.

Why Other Options Are Wrong:3000, 5600, 6600 are too large given r and h; 2100 neglects the π/3 factor; 2200 is consistent with π = 22/7.

Common Pitfalls:Using πr^2h (cylinder volume) instead of (1/3)πr^2h; arithmetic slips squaring r; rounding too early.

Final Answer:2200 cm^3