Question

A circle has an area of 153.86 units2 and a circumference of 43.96 units. If the radius is 7 units, what can be said about the relationship between the area and the circumference? (Use 3.14 for .) A. The ratio of the area to the circumference is equal to half the radius. B. The ratio of the area to the circumference is equal to twice the radius. C. The ratio of the area to the circumference is equal to the square root of the radius. D. The ratio of the area to the circumference is equal to the radius squared.

Answer 1

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

Explanation:

We are given that area of a circle=153.86 square units

Circumference of circle=43.96 units

Radius of circle=7 units

We have to find that the relation ship between area of circle and circumference of circle

Area of circle=
`\pi r^2`

Circumference of circle=
`2\pi r`

Ratio of area of circle to the circumference=
`(\pi r^2)/(2\pi r)`

Ratio of area of the circle to the circumference of the circumference=
`(1)/(2) r`

Ratio of area to the circumference=
`(153.86)/(43.96)=(7)/(2)=(r)/(2)`

Hence, option A is true.

Answer:A: The ratio of area of circle to the circumference is equal to half the radius.

Answer 2

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

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

The circumference of a circle is equal to

`C=2\pi r`

The ratio of the area to the circumference is equal to

`(A)/(C)=(\pi r^(2))/(2\pi r)`

Simplify

`(A)/(C)=(r)/(2)`

Verify

In this problem

`A=153.86\ units^(2)`

`C=43.96\ units`

`(A)/(C)=(153.86)/(43.96)=3.5\ units`

and
`3.5\ units` is equal to half the radius

therefore

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