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. Enter your answer in the box.

Answer 1

Answer:

37.69    (≈ 38 ft²)

Step-by-step explanation:

2πr = 30.77

r = 30.77 / (2 * 3.14) = 4.9

half of free-throw circle area: πr² / 2 = (3.14 * 4.9²) / 2 = 37.69    (≈ 38 ft²)

Answer 2

The area of the half of the free throw circle that will be painted gray for this case is 40 sq. ft approximately.

How to find the area of a semicircle?

A semicircle is half of a circle. Its surface is half of a full circle. Thus, its area is half of the area of a circle with same radius.

Let the radius of the semicircle be 'r' units, then the area of that semicircle would be:

$S = \dfrac{\pi r^2 }{2} \: \rm unit^2$

For this case, we're given that:

• The free throw circle has circumference of 30.77 ft
• Half of that free throw circle is going to get painted grey.
• We have to find the area of that half section which will be painted grey.

So, let we suppose that the radius of that circle is 'r' units.

Then, the circumference of that circle would be:

$C = 2 \pi r$ ft

As it is given that C = 30.77 ft, thus, we get:

$2\pi r = 30.77\\\\\text{Dividing both the sides by } 2\pi\\\\r = \dfrac{30.77}{2\pi} \approx \dfrac{30.77}{2 \times 3.14} \approx 4.9 \: \rm ft$

The area of a semicircle with radius 4.9 ft is:

$S = \dfrac{\pi (4.9)^2 }{2} \approx \dfrac{3.14 * 4.9}{2} \approx 37.6957 \approx 40\: \rm ft^2$ (rounded to the nearest sq. foot).

Thus, the area of the half of the free throw circle that will be painted gray for this case is 40 sq. ft approximately.

Learn more about area of a semicircle here:

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