Calculate the area, in square centimetres, of a circle whose radius is 10.5 centimetres. Use pi = 22/7.

Introduction / Context:
This question checks your ability to use the standard area formula for a circle when the radius is a decimal number. Circles with radius 10.5 centimetres are common in exam problems, because 10.5 can be written as 21/2 and simplifies nicely with pi = 22/7.

Given Data / Assumptions:

• Radius r = 10.5 centimetres.
• We must find the area A in square centimetres.
• Use pi = 22/7.

Concept / Approach:
The area A of a circle is given by:
A = pi * r^2.
Because r = 10.5, which is 21/2 as a fraction, squaring the radius gives a convenient rational number. We substitute r^2 into the area formula, multiply by pi, and then simplify to get the final area value in square centimetres.

Step-by-Step Solution:
Step 1: Express the radius as a fraction: r = 10.5 = 21 / 2. Step 2: Compute r^2: r^2 = (21 / 2)^2 = 441 / 4. Step 3: Use the formula A = pi * r^2. A = (22/7) * (441/4). Step 4: Simplify (22/7) * (441/4). First, 441 / 7 = 63, so we get 22 * 63 / 4. Compute 22 * 63 = 1386. So A = 1386 / 4 square centimetres. Step 5: Divide 1386 by 4 to get 346.5. Therefore, the area of the circle is 346.5 square centimetres.

Verification / Alternative check:
As a rough check, we can approximate pi as 3.14 and compute A approximately as 3.14 * (10.5)^2. Since (10.5)^2 is about 110.25, the approximate area is 3.14 * 110.25 which is close to 346.2 square centimetres. This is very close to 346.5, so the exact answer with pi = 22/7 is consistent with the approximate method.

Why Other Options Are Wrong:
Option A (693 cm2): This is exactly double the correct area and may come from mistakenly doubling the result. Option B (157.5 cm2): This is far too small and might arise from using radius instead of radius squared. Option C (315 cm2): This still underestimates the area and does not result from the correct formula. Option E (330 cm2): This is a rounded guess but does not match the exact computation.

Common Pitfalls:
Typical errors include using the diameter instead of the radius, forgetting to square the radius, or inserting pi as 3 instead of 22/7 or 3.14. When the radius is a decimal like 10.5, many students also make mistakes in squaring it. Converting 10.5 to 21/2 and then squaring makes the algebra more systematic and reduces calculation errors.

Final Answer:
The area of the circle is 346.5 cm2 (square centimetres).