In a right circular cylinder, the ratio of the curved surface area to the total area of its two circular bases is 2 : 1. If the total surface area of the cylinder is 23100 square centimetres, what is the volume of the cylinder in cubic centimetres?

Introduction / Context:
This numerical problem combines formulas for the surface area and volume of a right circular cylinder. By relating the curved surface area to the areas of the circular bases, we can derive a relationship between the radius and height. Using the given total surface area, we can then compute the cylinder volume. Such questions are common in aptitude tests to check understanding of solid geometry and algebraic manipulation.

Given Data / Assumptions:

Curved surface area of the cylinder = 2 * pi * r * h.
Total area of the two bases = 2 * pi * r^2.
Given ratio of curved surface area to total base area = 2 : 1.
Total surface area of the cylinder = 23100 square centimetres.
Take pi = 22 / 7 for calculation.

Concept / Approach:
Let r be the radius and h be the height of the cylinder. The given ratio of curved surface area to area of the two bases allows us to express h in terms of r. Once we know that relationship, we use the total surface area formula to solve for r. With r obtained, we can find h, and finally compute the volume V = pi * r^2 * h. The process involves careful algebraic simplification and substitution.

Step-by-Step Solution:
Curved surface area (CSA) = 2 * pi * r * h. Area of two bases = 2 * pi * r^2. Given CSA : base area = 2 : 1, so (2 * pi * r * h) / (2 * pi * r^2) = 2 / 1. Simplify the ratio: h / r = 2, hence h = 2r. Total surface area (TSA) = CSA + area of two bases = 2 * pi * r * h + 2 * pi * r^2. Substitute h = 2r: TSA = 2 * pi * r * 2r + 2 * pi * r^2 = 4 * pi * r^2 + 2 * pi * r^2 = 6 * pi * r^2. Given TSA = 23100, so 6 * pi * r^2 = 23100. Using pi = 22 / 7 gives 6 * (22 / 7) * r^2 = 23100. Then r^2 = 23100 * 7 / (6 * 22) = 1225, so r = 35 cm. From h = 2r, we get h = 70 cm. Volume V = pi * r^2 * h = (22 / 7) * 1225 * 70 = 269500 cubic centimetres.

Verification / Alternative check:
We can verify quickly by recomputing the total surface area with r = 35 and h = 70. The curved surface area becomes 2 * (22 / 7) * 35 * 70 = 15400 square centimetres. The total area of the two bases is 2 * (22 / 7) * 35^2 = 7700 square centimetres. The ratio 15400 : 7700 simplifies to 2 : 1 as required, and their sum 15400 + 7700 = 23100 matches the given total surface area.

Why Other Options Are Wrong:
247200 corresponds to an incorrect relationship between radius and height, often from algebraic mistakes when using the ratio condition.
312500 and 341800 arise from misusing the pi value, mixing square and cubic units, or incorrectly computing r^2 from the total surface area equation.
196350 is too small and typically comes from halving or misinterpreting the base area contribution in the total surface area formula.

Common Pitfalls:
Students often confuse the curved surface area formula with the total surface area and may forget that two bases contribute to TSA. Another frequent error is to cancel pi and r incorrectly in the ratio, which leads to wrong relationships between h and r. Some learners also plug in pi as 3.14 instead of 22 / 7, which can produce close but nonmatching options. Being systematic with algebra and unit consistency avoids these mistakes.

Final Answer:
The volume of the cylinder is 269500 cubic centimetres.