Question

Roderick wants to draw a circle for which the numerical value of the circumference is greater than the value of the area. Which lengths could he use for the radius? Check all that apply.

Answer 1

Answer:

The length of the radius must be less than $2$

$\frac{1}{2},1,1.5$

Step-by-step explanation:

we know that

The circumference of a circle is equal to

$C=2\pi r$

The area of a circle is equal to

$A=\pi r^{2}$

where r is the radius of the circle

In this problem we have that

$C > A$

Substitute

$2\pi r > \pi r^{2}$

Simplify

$2r > r^{2}$

$2> r$ ------> rewrite

$r< 2\ units$

The length of the radius must be less than $2$

the answer is

$\frac{1}{2},1,1.5$

Answer 2

The best way to justify which answers are correct are to calculate the circumference and the area for each of the circles with the given radii. I organized this information into a chart.

Circumference | Area

1/2 3.14 0.785

1 6.28 3.14

1 1/2 9.42 7.065

2 12.56 12.56

2 1/2 15.7 19.625

The first three choices will result in a numerical value for the radius that is smaller than the area.