4.
This model of the backboard of a basketball goal is composed of a rectangle and a semicircle. Use the ruler provided to measure the dimensions of the model to the nearest half inch.
Which measurement is closest to the area of the model of the backboard in square inches?
18.56 in.2
31.12 in.2
12.28 in.2
23.56 in.2
To determine the closest measurement to the area of the model of the backboard in square inches, we first need to calculate the area of the backboard model.
The backboard model consists of a rectangle and a semicircle. The area of the rectangle can be calculated using the formula A = l*w, where l is the length and w is the width.
From the measurements provided in the previous question, the length of the rectangle is approximately 18 inches and the width is approximately 7 inches.
Therefore, the area of the rectangle is 18 * 7 = 126 square inches.
Next, we need to calculate the area of the semicircle. The formula for the area of a semicircle is A = 1/2 * π * r^2, where r is the radius.
The radius of the semicircle can be calculated as half of the width of the rectangle, which is 7 inches. Therefore, the radius is 7/2 = 3.5 inches.
Plugging in the values, the area of the semicircle is 1/2 * π * (3.5)^2 ≈ 6.06 square inches.
Adding the area of the rectangle and the area of the semicircle, the total area of the backboard model is approximately 126 + 6.06 = 132.06 square inches.
Given the options, the closest measurement to the area of the model of the backboard in square inches is 18.56 in^2.