The ratio of curved surface area to total surface area of a right circular cylinder is 2:5. If the total surface area is 3080 cm^2, what is the volume of the cylinder (in cm^3)?

Introduction / Context:
This question combines cylinder surface-area formulas with ratio reasoning. The ratio CSA:TSA = 2:5 immediately gives a relationship between height and radius, and then the given TSA lets us compute the exact radius. Finally, volume follows from V = pi*r^2*h. This is a classic multi-step mensuration problem.

Given Data / Assumptions:

• CSA:TSA = 2:5
• TSA = 3080 cm^2
• CSA = 2*pi*r*h
• TSA = 2*pi*r*(h + r)
• Use pi = 22/7 (standard for such options)

Concept / Approach:
Use the ratio to connect CSA and TSA, then derive h in terms of r using TSA/CSA = (h + r)/h. Use CSA to find r, then compute volume.

Step-by-Step Solution:

Verification / Alternative check:
Check TSA using r = 7*sqrt(6) and h = (2/3)r: TSA becomes 3080 cm^2 exactly (with pi = 22/7), confirming consistency.

Why Other Options Are Wrong:

Common Pitfalls:
Mixing CSA with TSA, forgetting the 2*pi*r factor cancels in the ratio, or using (2/5) incorrectly as (5/2).

Final Answer:
4312*sqrt(6)