The curved surface area of a right circular cylinder is 440 square centimetres. If the circumference of its base is 44 centimetres, what is the volume of the cylinder? (Take π = 22/7.)

Introduction / Context:
This question links curved surface area, circumference, and volume of a right circular cylinder. It tests your ability to relate the various formulas for a cylinder and to work backwards from surface information to find the volume, using the fact that the curved surface area can be expressed in terms of the base circumference and height.

Given Data / Assumptions:

• Curved surface area (CSA) of the cylinder = 440 square centimetres.
• Circumference of the base = 44 centimetres.
• Take π = 22/7.
• We need the volume of the cylinder in cubic centimetres.

Concept / Approach:
Two key facts are useful:

• Curved surface area of a cylinder = 2 * π * r * h = (circumference of base) * h.
• Volume of a cylinder = π * r^2 * h.

We are given the curved surface area and the base circumference, so we can first find the height h by dividing CSA by the circumference. Then we use the circumference to find the radius r, and finally we substitute r and h into the volume formula.

Step-by-Step Solution:
Step 1: Use CSA = (circumference) * height. Given CSA = 440 and circumference = 44, we have 440 = 44 * h. Step 2: Solve for h: h = 440 / 44 = 10 cm. Step 3: Use circumference formula to find radius: circumference = 2 * π * r = 44. Step 4: Substitute π = 22/7: 2 * (22/7) * r = 44. Step 5: Simplify 2 * 22/7 = 44/7, so (44/7) * r = 44. Step 6: Multiply both sides by 7 / 44: r = 44 * (7 / 44) = 7 cm. Step 7: Now compute volume: V = π * r^2 * h = (22/7) * 7^2 * 10. Step 8: Evaluate r^2 = 49, so V = (22/7) * 49 * 10 = (22/7) * 490. Step 9: Simplify 490 / 7 = 70, so V = 22 * 70 = 1540 cubic centimetres.

Verification / Alternative check:
As a consistency check, we can re compute the curved surface area using r = 7 cm and h = 10 cm. CSA = 2 * π * r * h = 2 * (22/7) * 7 * 10 = 2 * 22 * 10 = 440 square centimetres, which matches the given value. This confirms that the derived radius and height are correct and that the volume calculation is reliable.

Why Other Options Are Wrong:
Volumes 770, 2310, and 3080 cubic centimetres would result from using incorrect values for height or radius, or from errors in the formula. For example, 770 cubic centimetres is only half the correct volume, suggesting a missing factor of 2. Volumes 2310 and 3080 do not satisfy the combined constraints of the given CSA and circumference. Only 1540 cubic centimetres is consistent with all given information.

Common Pitfalls:
A common error is to misinterpret the curved surface area as total surface area and include the areas of the circular bases. Another mistake is to attempt to solve for radius and height simultaneously using the CSA formula alone, without exploiting the simple relationship CSA = (circumference) * height. Some learners also miscalculate when simplifying fractions involving π. Carefully separating each step and using the given circumference directly makes the problem straightforward.

Final Answer:
The volume of the cylinder is 1540 cubic centimetres.