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The area of a circle is 616 cm². Find its circumference (Take π = 22/7).
88 cm
44 cm
132 cm
176 cm
88 cm
Use the standard ratio 7: 44 for radius to circumference: if radius is 7, area is 154 and circumference is 44. Since the given area is 616 (154×4), the linear scale factor is 4=2, making the circumference 44×2=88 cm.
Area of the circle = 616 cm², π=722
A=πr2,C=2πr
Use the standard ratio 7: 44 for radius to circumference: if radius is 7, area is 154 and circumference is 44. Since the given area is 616 (154×4), the linear scale factor is 4=2, making the circumference 44×2=88 cm.
Students often forget to take the square root of the area ratio when scaling up radius and circumference, or they confuse area and circumference formulas.
Write the area formula and substitute the given values
Start with the formula for the area of a circle and plug in the known area and the value of π.
616=722×r2
Solve for the radius r
Isolate r2 by multiplying both sides by 7 and dividing by 22.
r2=22616×7=28×7=196
Calculate the positive square root for the radius
Take the square root of both sides to find the radius r.
r=196=14 cm
Calculate the circumference
Substitute the radius r=14 into the circumference formula C=2πr.
C=2×722×14=88 cm
A is correct because the calculated circumference of the circle is 88 cm.
Understanding circle measurements and radius scaling is crucial for solving mensuration problems involving cylinders, cones, and spheres in railway exams.
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