MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

Answer:Option A. The ratio of the area to the circumference is equal to half the radiusStep-by-step explanation:we know thatThe area of a circle is equal to[tex]A=\pi r^{2}[/tex]The circumference of a circle is equal to[tex]C=2\pi r[/tex]The ratio of the area to the circumference is equal to[tex]\frac{A}{C}=\frac{\pi r^{2}}{2\pi r}[/tex]Simplify[tex]\frac{A}{C}=\frac{r}{2}[/tex]VerifyIn this problem[tex]A=153.86\ units^{2}[/tex][tex]C=43.96\ units[/tex][tex]\frac{A}{C}=\frac{153.86}{43.96}=3.5\ units[/tex]and [tex]3.5\ units[/tex] is equal to half the radius thereforeThe ratio of the area to the circumference is equal to half the radius