Question

A basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet, what is the area that will be painted grey? Use 3.14 for π, and round to the nearest square foot.

Answer 1

Answer:

The area that will be painted grey is $4 \ ft^2$.

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;

$2\pi r= 30.77$

Dividing both side by 2π we get;

$\frac{2\pi r}{2\pi}=\frac{30.77}{2\pi}\\\\r \approx 4.9 ft$

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 = $\frac{1}{2}\pi r^2= \frac{1}{2}\pi \times 4.9^2 = 3.82ft^2$

Rounding to nearest foot we get;

area that will be painted grey = $4 \ ft^2$

Hence The area that will be painted grey is $4 \ ft^2$.