Answer:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
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:

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:

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 =

Initial area =

After doubling:
Radius = 14 cm
circumference =
(Twice the initial circumference)
area =
(4 times the initial area)
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Formula for Circumference of a circle in form of Diameter:

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:

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 =

Initial area =

After doubling:
Diameter = 56 cm
circumference =
(Twice the initial circumference)
area =
(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.