Difficulty: Easy
Correct Answer: 616 sq cm
Explanation:
Introduction / Context:
This is a straightforward circle mensuration problem. You are given the diameter of a circle and asked to find its area using the common approximation π = 22/7. It tests your ability to convert diameter to radius and correctly apply the area formula for a circle with the specified value of π.
Given Data / Assumptions:
Concept / Approach:
The first step is to find the radius, which is half of the diameter. The area formula requires the radius squared multiplied by π. Using the value π = 22/7 keeps the arithmetic with denominators manageable because the radius will be a multiple of 7, leading to easy cancellation and an exact integer result for the area in this case.
Step-by-Step Solution:
Diameter d = 28 cm.
Radius r = d / 2 = 28 / 2 = 14 cm.
Area A = πr^2 = (22/7) * 14^2.
Compute 14^2 = 196.
So A = (22/7) * 196.
Simplify 196 / 7 = 28.
Therefore A = 22 * 28 = 616 sq cm.
Verification / Alternative check:
As a quick check, note that 28 is 4 times 7, so r = 14 is 2 times 7. Squaring r gives 196, and multiplying 196 by 22/7 is equivalent to dividing 196 by 7 to get 28 and then multiplying by 22. There are no fractions in the final step, which reduces the chance of arithmetic errors. This confirms the exact result of 616 square centimetres.
Why Other Options Are Wrong:
308 sq cm and 154 sq cm: These correspond to halving or quartering the correct area, possibly from misusing diameter instead of radius or missing a factor of 2.
77 sq cm: Much too small and likely comes from confusing circumference with area or misusing the formula.
704 sq cm: Larger than the correct area and does not result from any correct application of A = πr^2 with the given numbers.
Common Pitfalls:
Using the diameter directly in the area formula instead of the radius.
Forgetting to square the radius before multiplying by π.
Miscalculating 14^2 or failing to cancel 196 with 7 correctly.
Final Answer:
The area of the circle is 616 sq cm
Discussion & Comments