Find the volume, in cubic centimetres, of a right circular cylinder whose diameter is 21 centimetres and whose height is 10 centimetres. Take pi = 22/7.

Introduction / Context:
This question tests your ability to compute the volume of a right circular cylinder using the standard formula. It also checks whether you correctly handle radius when only the diameter is given. Volume questions like this are common in quantitative aptitude and basic geometry sections.

Given Data / Assumptions:

• Diameter of the cylinder = 21 centimetres.
• Radius r = diameter / 2 = 21 / 2 = 10.5 centimetres.
• Height h = 10 centimetres.
• We must find the volume in cubic centimetres.
• Use pi = 22/7.

Concept / Approach:
The volume V of a right circular cylinder is given by:
V = pi * r^2 * h.
We first compute the radius from the diameter, then square the radius, multiply by pi and the height. Because the radius is a decimal (10.5), it is convenient to convert it to a fraction to simplify the algebra. Once we compute the exact value, we compare it with the options to select the correct one.

Step-by-Step Solution:
Step 1: Radius r = 21 / 2 = 10.5 centimetres. Step 2: Express r as a fraction: r = 21 / 2, so r^2 = (21 / 2)^2 = 441 / 4. Step 3: Use the formula V = pi * r^2 * h. V = (22/7) * (441/4) * 10. Step 4: Simplify (22/7) * (441/4). First, 441 / 7 = 63, so this becomes 22 * 63 / 4. 22 * 63 = 1386, so we have 1386 / 4. 1386 / 4 = 346.5. Step 5: Now multiply by the height h = 10: V = 346.5 * 10 = 3465 cubic centimetres.

Verification / Alternative check:
We can do a quick approximation by using pi as 3.14. Then V is approximately 3.14 * (10.5)^2 * 10. Since (10.5)^2 is about 110.25, the volume is roughly 3.14 * 110.25 * 10, which is about 3463.85 cubic centimetres. This is very close to 3465, confirming that 3465 cm3 is a reasonable and correct choice given pi = 22/7.

Why Other Options Are Wrong:
Option A (3118 cm3): This is too low and does not match the exact computation using the correct formula. Option B (3275 cm3): This is also lower than the correct value and may arise from rounding pi incorrectly. Option C (3621 cm3): This is somewhat higher than the correct result and does not align with the exact calculation. Option E (3300 cm3): This is a rounded looking number but still does not match the correctly derived volume.

Common Pitfalls:
Common errors include using the diameter directly in place of the radius, forgetting to divide by 2 to find the radius, or using the surface area formula instead of the volume formula. Some students also forget to square the radius and only multiply by r once. Carefully writing the formula V = pi * r^2 * h and substituting r as 21 / 2 helps avoid these mistakes.

Final Answer:
The volume of the cylinder is 3465 cm3 (cubic centimetres).