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The area of a circle whose circumference is 88 cm is:
616 cm²
308 cm²
154 cm²
1232 cm²
616 cm²
Use the standard ratio where a circle with radius 7 cm has circumference 44 cm and area 154 cm². Since the circumference is doubled (88 cm), the radius is 14 cm, and the area increases by a factor of 22=4 (154×4=616 cm²).
Circumference of the circle C = 88 cm
C=2πr
Use the standard ratio where a circle with radius 7 cm has circumference 44 cm and area 154 cm². Since the circumference is doubled (88 cm), the radius is 14 cm, and the area increases by a factor of 22=4 (154×4=616 cm²).
Forgetting to square the scaling factor when the circumference doubles, or confusing the formulas for circumference and area.
Find the Radius
Use the circumference formula C=2πr with C=88 cm to set up the equation for radius r.
88=2×722×r
Calculate Radius Value
Isolate r and solve the equation to find the exact radius in centimeters.
r=4488×7=14 cm
Calculate Area
Substitute the radius r=14 cm into the area formula A=πr2 to get the final result.
A=722×142=616 cm2
A is correct because the radius is calculated as 14 cm from the circumference of 88 cm, leading to an area of 616 cm².
Understanding scaling factors in area and volume helps save time in mensuration questions involving similar figures.
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