Two common mistakes in calculations are related to the circumference
and area of a circle
When giving calculations
for the circumference and area of a circle I usually give the following two
calculations.
1) Find
the circumference of a circle with radius 14 cm.
2) Find
the area of a circle with diameter 14 cm.
Most students make two
types of mistakes in both calculations.
For one, they would
have changed the formulas for the circumference and area of a circle and done the
calculation. That is, they would have done the calculation using either the
perimeter-to-area formula or the area-to-perimeter formula.
For second, in the
interest of doing quick calculations, the second calculation is diameter of 14
cm. They would have ignored the word diameter and considered it as radius and
done the calculation.
We should note that
both the formulas for the circumference and the area of a circle involve the
radius and not the diameter. Therefore, in the calculations related to the
circumference or area of the circle, we should make sure whether the diameter or
radius is given and then proceed with the calculation. When the diameter is given,
divide it by two to convert it to radius. If you rush to consider the diameter
as the radius, the calculation will be wrong, won't it?
I have seen empirically
that asking students to do these two calculations and pointing out the mistakes
they made in them improves their understanding rather than explaining them.
So what I request you
too is to do both the above calculations.
After doing check your
account steps and answers below.
|
1) 14 cm. Find the circumference of a circle with radius. Solution: The
radius of the circle is r = 14 cm. Circumference
of circle = 2πr unit = 2 ×
(22 / 7) × 14 = 88 cm |
2) 14 cm. Find the area of a circle with diameter. Solution: Diameter
of the circle is d = 14 cm. The
radius of the circle is r = 14 / 2 = 7 cm. Area
of circle = πr2 square unit = (22 / 7) × 7 ×7 =
154 sq. cm |
Next we
will look at finding the area of a quadrilateral tomorrow.
*****
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