Question

Select all of the true statements. Group of answer choices LaTeX: \piπππ π π is the area of a circle with a diameter of 1. LaTeX: \piπ π ππ π π is the area of a circle with a radius of 1. LaTeX: \piππππ is the circumference of a circle with a radius of 1. LaTeX: \piπππ π π is the constant of proportionality relating the radius of a circle to its area. LaTeX: \piπ π ππ π π is the circumference of a circle with a diameter of 1. LaTeX: \piπππ π π is the constant of proportionality relating the diameter of a circle to its circumference.

Answer 1

Options:

A. π is the area of a circle with a radius of 1.

B. π is the circumference of a circle with a radius of 1.

C. π is the constant of proportionality relating the radius of a circle to its area.

D. π is the circumference of a circle with a diameter of 1.

E. π is the constant of proportionality relating the diameter of a circle to its circumference.

Answer:

A, C, D, E

Explanation:

Analyzing the options, one after the other.

A.

Area is calculated as thus:

`Area = \pi r^2`

In this case,

`r = 1`

So: we have

`Area = \pi * 1^2`

`Area = \pi * 1`

`Area = \pi`

This option is true

B.

Circumference is calculated as thus:

`C = 2\pi r`

In this case

`r = 1`

So, we have:

`C = 2\pi * 1`

`C = 2\pi`

This option is false

C.

Area is calculated as thus:

`Area = \pi r^2`

In this formula, Area and Radius can change but
`\pi` remains constant.

Hence, this option is true

D.

Circumference is calculated as thus:

`C = 2\pi r` or
`C = \pi d`

Where
`d = diameter`

In this case

`d = 1`

So, we have:

`C = \pi * 1`

`C = \pi`

Hence, this option is true

E.

Circumference is calculated as thus:

`C = 2\pi r` or
`C = \pi d`

Where
`d = diameter`

Considering

`C = \pi d`

In this formula, Circumference and Diameter can change but
`\pi` remains constant.

Hence, this option is true