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

Step-by-step 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