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The area of a circle with a diameter of 28 cm is:
616 ┬аsq┬аcm
154 ┬аsq┬аcm
1232 ┬аsq┬аcm
308 ┬аsq┬аcm
616 ┬аsq┬аcm
Use the standard ratio for circles: when diameter is 14 cm, area is 154 cm┬▓. Since the diameter here is 28 cm (double), the area increases by a factor of 22=4, giving 154├Ч4=616┬аsq┬аcm.
Diameter of the circle d = 28 cm
Area=╧Аr2
Use the standard ratio for circles: when diameter is 14 cm, area is 154 cm┬▓. Since the diameter here is 28 cm (double), the area increases by a factor of 22=4, giving 154├Ч4=616┬аsq┬аcm.
Using the diameter directly in the area formula instead of first finding the radius (r=2dтАЛ=14┬аcm), or squaring the diameter directly without dividing by 4.
Find the radius
The radius is half of the diameter. Given d=28┬аcm, we find the radius r.
r=228тАЛ=14┬аcm
Apply the area formula
Substitute the value of the radius into the area of a circle formula Area=╧Аr2, using ╧А=722тАЛ.
Area=722тАЛ├Ч(14)2
Calculate the final area
Simplify the expression by expanding 142 as 14├Ч14 and cancelling out the denominator.
Area=722тАЛ├Ч196=22├Ч28=616┬аsq┬аcm
A is correct because the calculated area of the circle is 616┬аsq┬аcm.
Understanding circle measurements and scaling factors is crucial for mensuration problems in CBT-1, often extending to cylinders and spheres in surface area and volume topics.
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