Question

Half of circle is called a semicircle.a semicircle has a diameter of 30 inches.what is the area of the window to the nearest square inch

Answer 1

To calculate the area of a semicircle with a diameter of 30 inches, first find the radius, which is 15 inches. Using the formula for the area of a circle (πr²) and dividing it by 2 because it's a semicircle, we find that the area is approximately 353 square inches to the nearest square inch.

Step-by-step explanation:

Calculating the Area of a Semicircle

The student question pertains to finding the area of a semicircle, which is inherently a geometry problem. Given the diameter of the semicircle is 30 inches, we first need to find the radius. The radius (r) is half of the diameter, so in this case, the radius is 15 inches. The area (A) of a circle is calculated using the formula A = πr². However, since we only have half of a circle, we need to divide this by 2 to get the area of the semicircle. Thus, the area of the semicircle is ½ * π * (15 inches)².

Performing the calculation, we find:

A = ½ * π * 225 sq inches

A ≈ ½ * 3.14159 * 225

A ≈ 353.429 sq inches

To the nearest square inch, the area of the semicircle is therefore approximately 353 square inches.

Answer 2

`A=353\ in^2`

Step-by-step explanation:

The question is

A window is shaped like a semicircle with a diameter of 30 inches. What is the area of the window? Round to the nearest square inch

we know that

The area of semicircle is equal to

`A=(1)/(2)\pi r^(2)`

we have

`r=30/2=15\ in` ---> the radius is half the diameter

substitute

`A=(1)/(2)\pi (15)^(2)`

`A=112.5\pi\ in^2`

assume

`\pi =3.14`

`A=112.5(3.14)=353,25\ in^2`

Round to the nearest square inch

`A=353\ in^2`