Question

A circle has an area of 200.96 units2 and a circumference of 50.24 units. If the radius is 8 units, what can be said about the relationship between the area and the circumference? (Use 3.14 for pi.)

A.

The ratio of the area to the circumference is equal to the square root of the radius.


B.

The ratio of the area to the circumference is equal to the radius squared.


C.

The ratio of the area to the circumference is equal to half the radius.


D.

The ratio of the area to the circumference is equal to twice the radius.

Answer 1

C. The ratio of the area to the circumference is equal to half the radius.

Explanation:

The area of a circle can be written as;

Area A = πr^2

The circumference of a circle is;

Circumference C = 2πr

Using the formula, w can derive the relationship between the two variables.

A = kC

k = A/C

Substituting the two formulas;

k = (πr^2)/(2πr) = r/2

So,

A = (r/2)C

A/C = r/2

The ratio of the area to the circumference is equal to half the radius.

Given;

Area = 200.96

Circumference = 50.24

Radius = 8

To confirm;

k = r/2 = 8/2 = 4

Also,

A/C = 200.96/50.24

A/C = 4