Answer:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
Step-by-step explanation:
Given that
Radius of a circle is doubled.
Diameter of circle is doubled.
To study:
The effect on circumference and area on doubling the radius and diameter.
Solution/explanation:
Let us discuss about the formula for circumference and area.
Formula for Circumference of a circle in form of radius:
[tex]C =2\pi r[/tex]
It is a linear equation in 'r'. So by doubling the radius will double the circumference.
Formula for Area of a circle in form of radius:
[tex]A =\pi r^2[/tex]
It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.
Testing using example:
Let the initial radius of a circle = 7 cm
Initial circumference = [tex]2 \times \frac{22}{7} \times 7 = 44 cm[/tex]
Initial area = [tex]\frac{22}{7} \times 7 \times 7 =154 cm^2[/tex]
After doubling:
Radius = 14 cm
circumference = [tex]2 \times \frac{22}{7} \times 14 = 88 cm[/tex] (Twice the initial circumference)
area = [tex]\frac{22}{7} \times 14 \times 14 =616 cm^2[/tex] (4 times the initial area)
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Formula for Circumference of a circle in form of Diameter:
[tex]C =\pi D[/tex]
It is a linear equation in 'D'. So by doubling the diameter will double the circumference.
Formula for Area of a circle in form of diameter:
[tex]A =\dfrac{1}{4}\pi D^2[/tex]
It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.
Testing using example:
Let the initial diameter of a circle = 28 cm
Initial circumference = [tex]\frac{22}{7} \times 28 = 88 cm[/tex]
Initial area = [tex]\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2[/tex]
After doubling:
Diameter = 56 cm
circumference = [tex]\frac{22}{7} \times 56= 176 cm[/tex] (Twice the initial circumference)
area = [tex]\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2[/tex] (4 times the initial area)
So, the answer is justified:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
