Question

a basketball court is a rectangle that is 28 m long and 15 m wide. a diagram on a coordinate plane shows a circle in the middle of the court centered at (0 m, 0 m). the point (0.8 m, 1.5 m) is on the circumference of the circle. approximately what percentage of the court does the circle cover? choose 1 answer: a 1% b 2% c 3% d 4%

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is $A_{r}=l\times w$, where $l = 28$m and $w = 15$m. So $A_{r}=28\times15=420$m².

Step2: Calculate the radius of the circle

The distance formula from the origin $(0,0)$ to the point $(x,y)=(0.8,1.5)$ on the circle is $r=\sqrt{x^{2}+y^{2}}$. So $r=\sqrt{0.8^{2}+1.5^{2}}=\sqrt{0.64 + 2.25}=\sqrt{2.89}=1.7$m.

Step3: Calculate the area of the circle

The area formula for a circle is $A_{c}=\pi r^{2}$, with $r = 1.7$m. So $A_{c}=\pi\times(1.7)^{2}\approx3.14\times2.89 = 9.0746$m².

Step4: Calculate the percentage

The percentage $P=\frac{A_{c}}{A_{r}}\times100\%=\frac{9.0746}{420}\times100\%\approx2.16\%$.

Answer:

B. 2%