Question

You double the radius of a circle. Predict what will happen tothe circle’s circumference and what will happen to its area. Test yourprediction for a few circles. Use a different radius for each circle. Thenpredict how doubling a circle’s diameter will affect its circumferenceand area. Test your prediction for a few circles with different diameters.

Answer 1

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:

`C =2\pi r`

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:

`A =\pi r^2`

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 =
`2 * (22)/(7) * 7 = 44 cm`

Initial area =
`(22)/(7) * 7 * 7 =154 cm^2`

After doubling:

Radius = 14 cm

circumference =
`2 * (22)/(7) * 14 = 88 cm` (Twice the initial circumference)

area =
`(22)/(7) * 14 * 14 =616 cm^2` (4 times the initial area)

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Formula for Circumference of a circle in form of Diameter:

`C =\pi D`

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:

`A =(1)/(4)\pi D^2`

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 =
`(22)/(7) * 28 = 88 cm`

Initial area =
`(1)/(4)* (22)/(7) * 28 * 28 =616cm^2`

After doubling:

Diameter = 56 cm

circumference =
`(22)/(7) * 56= 176 cm` (Twice the initial circumference)

area =
`(1)/(4)* (22)/(7) * 56 * 56 =2464cm^2` (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.