Right circular cone — find base diameter from volume and height: The volume of a right circular cone is 48π cm3 and its height is 9 cm. Compute the diameter of the circular base (in centimeters).

Introduction / Context:This is a direct application of the cone volume formula with one unknown (the base radius). Once the radius is determined, the base diameter is twice the radius.

Given Data / Assumptions:

• Height h = 9 cm.
• Volume V = 48π cm3.
• For a right circular cone, V = (1/3) * π * r^2 * h.
• All dimensions are in centimeters; π is symbolic (exact cancellation occurs).

Concept / Approach:Rearrange the cone volume formula to isolate r^2. Then compute the diameter D = 2r. The calculation is purely algebraic and does not need any approximation to π since π cancels out.

Step-by-Step Solution:V = (1/3) * π * r^2 * h48π = (1/3) * π * r^2 * 948π = 3π * r^2 ⇒ r^2 = 48/3 = 16r = 4 cm ⇒ D = 2r = 8 cm

Verification / Alternative check:Substitute r = 4, h = 9 back into V: (1/3)*π*16*9 = (1/3)*π*144 = 48π cm3, exactly as given.

Why Other Options Are Wrong:4 cm is the radius, not diameter; 7 cm and 11 cm are arbitrary; they do not satisfy the cone volume with h = 9 cm.

Common Pitfalls:Confusing radius with diameter; forgetting that r^2 appears in the formula; attempting to approximate π unnecessarily.

Final Answer:8 cm