The circumference of the circular base of a solid cylinder is 44 cm and its height is 15 cm. What is the volume of the cylinder in cubic centimetres?

Introduction / Context:
This problem asks for the volume of a cylinder when the circumference of its base and its height are given. Instead of giving the radius directly, the question provides the circumference, so we must first relate circumference to radius and then use the volume formula. This tests understanding of multiple circle formulas and how to combine them correctly.

Given Data / Assumptions:

• Circumference of the base, C = 44 cm.
• Height of the cylinder, h = 15 cm.
• The base is a circle of radius r.
• We must find the volume in cubic centimetres.

Concept / Approach:
For a circle, the circumference is related to the radius by:
C = 2 * pi * r For a cylinder, the volume V is given by:
V = pi * r^2 * h Here, we first express r in terms of C and pi, then substitute into the volume formula. Alternatively, we can use a derived formula expressing volume directly in terms of circumference and height: V = (C^2 * h) / (4 * pi). Both approaches give the same result when done carefully.

Step-by-Step Solution:
Given C = 44 cm. From C = 2 * pi * r, r = C / (2 * pi) = 44 / (2 * pi) = 22 / pi. Volume V = pi * r^2 * h. Substitute r = 22 / pi and h = 15: V = pi * (22 / pi)^2 * 15. V = pi * (484 / pi^2) * 15 = (484 * 15) / pi. Compute numerator: 484 * 15 = 7260. So V = 7260 / pi cubic centimetres. Using pi ≈ 3.14159, V ≈ 7260 / 3.14159 ≈ 2311 cubic centimetres.

Verification / Alternative check:
Alternatively, we can approximate r using pi ≈ 22 / 7: r = 44 / (2 * 22 / 7) = 44 * 7 / 44 = 7 cm. Then V ≈ pi * 7^2 * 15 ≈ 3.14 * 49 * 15 ≈ 3.14 * 735 ≈ 2309.9 cm^3, very close to 2311 cm^3. The small difference is due to different approximations of pi, and 2311 cubic cm is a reasonable rounded value.

Why Other Options Are Wrong:
The other options 2759, 2247 and 2614 cubic cm do not correspond to V = 7260 / pi with any standard approximation of pi. They reflect miscalculations such as using an incorrect value of radius or applying the area formula incorrectly. 2000 cubic cm is clearly too small for a cylinder of this circumference and height.

Common Pitfalls:
Students may incorrectly treat the given circumference as the diameter or directly plug it in as the radius. Others forget to square r in the volume formula or mishandle the division by pi. It is also easy to make arithmetic mistakes when multiplying or dividing large numbers, so careful calculation is important.

Final Answer:
The volume of the cylinder is approximately 2311 cubic cm.