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If a circle has a diameter of 14 cm, what is its area? (Take π = 22/7)
154 cm²
144 cm²
164 cm²
134 cm²
154 cm²
Since the diameter is a multiple of 7, use the rule that for a radius of 7 cm, the area is 154 cm². If radius is r=n×7, area is 154×n2. Here r=7, so area = 154 cm².
Diameter of the circle (d) = 14 cm, Value of constant π = 22/7
Area=π×r2
Since the diameter is a multiple of 7, use the rule that for a radius of 7 cm, the area is 154 cm². If radius is r=n×7, area is 154×n2. Here r=7, so area = 154 cm².
A frequent error is to use the diameter directly in the area formula (Area=π×d2) instead of converting it to the radius first (r=d/2).
Calculate the radius
The radius (r) is half of the diameter (d). Given d=14 cm, we calculate r=14/2.
r=214=7 cm
Apply the area formula
Substitute the radius (r=7) and the given π=22/7 into the area formula: Area=π×r2.
Area=722×7×7
Simplify and solve
Cancel the 7 in the numerator and denominator to get 22×7.
Area=22×7=154 cm2
A is correct because calculating with a radius of 7 cm yields an area of 154 cm².
This concept of working with multiples of 7 (especially when π = 22/7 is given) is essential for solving problems involving circumferences and areas of circles quickly in time-bound exams.
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