Question

PLSS GEOMETRY 50POINTS ​

Answer 1

C) 1589.63 sq cm

Explanation:

To find the area of the circular dart board, we can use the formula for the area of a circle. The formula for the area of a circle is:

`\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}`.

The diameter of a circle is twice its radius.

Given that the diameter of the dart board is 45 cm, calculate the radius by dividing the diameter by 2:

`r = (45)/(2)= 22.5 \;\sf cm`

To find the area of the dart board, substitute the value of r into the area formula (using 3.14 for pi):

`\begin{aligned}\implies A &= \pi r^2\\&=3.14 \cdot (22.5)^2\\&= 3.14 \cdot 506.25\\&=1589.625\\&=1589.63\; \sf sq \; cm \; (nearest\;hundredth)\end{aligned}`

Therefore, the area of the dart board is approximately 1589.63 square centimeters, rounded to the nearest hundredth.