Volume of a hemisphere (radius 3 cm): Calculate the volume in cubic centimeters.

Introduction / Context:The hemisphere’s volume is half that of a sphere with the same radius. It checks recall of V_sphere and the 1/2 factor for a hemisphere.

Given Data / Assumptions:

• r = 3 cm
• V_sphere = (4/3)πr^3
• V_hemisphere = (1/2) * V_sphere

Concept / Approach:Plug r = 3 into the sphere formula and then take half for the hemisphere.

Step-by-Step Solution:V_sphere = (4/3)π * 27 = 36π cm^3V_hemisphere = 36π / 2 = 18π cm^3

Verification / Alternative check:Known template: hemisphere volume = (2/3)πr^3; substituting r = 3 gives (2/3)π * 27 = 18π cm^3, same result.

Why Other Options Are Wrong:4/3 π cm^3 omits r^3; 13π is arbitrary; 19/π is dimensionally wrong; 9π is half the hemisphere’s volume (quarter of a sphere).

Common Pitfalls:Forgetting to halve the sphere’s volume; using surface area instead of volume.

Final Answer:18π cm^3