Respuesta :
Answer:
The area that will be painted grey is [tex]4 \ ft^2[/tex].
Step-by-step explanation:
Given:
Circumference of the free-throw circle= 30.77 feet
we need to find the area that will be painted grey.
Solution:
First we will find the radius (r).
Now we know that circumference of the circle is 2 times π times radius (r).
Framing in equation form we get;
[tex]2\pi r= 30.77[/tex]
Dividing both side by 2π we get;
[tex]\frac{2\pi r}{2\pi}=\frac{30.77}{2\pi}\\\\r \approx 4.9 ft[/tex]
Now given:
A basketball team wants to paint half of a free-throw circle grey.
So we will use the formula for semicircle.
Area of semicircle is half times π times square of the radius (r).
framing in equation form we get;
area that will be painted grey = [tex]\frac{1}{2}\pi r^2= \frac{1}{2}\pi \times 4.9^2 = 3.82ft^2[/tex]
Rounding to nearest foot we get;
area that will be painted grey = [tex]4 \ ft^2[/tex]
Hence The area that will be painted grey is [tex]4 \ ft^2[/tex].
