Find the area of a circle with a diameter of 16 inches. Use 3.14 for pi.
A. $50.24 in ^2$
B. $100.48 in ^2$
C. $200.96 in ^2$
D. $251.2 in ^2$
Answer (1)
Calculate the radius by dividing the diameter by 2: r = 2 16 = 8 inches.
Calculate the area using the formula A = π r 2 .
Substitute the values: A = 3.14 × 8 2 .
The area of the circle is 200.96 in 2 .
Explanation
Problem Analysis and Given Data We are given a circle with a diameter of 16 inches, and we need to find its area using π = 3.14 . The formula for the area of a circle is A = π r 2 , where r is the radius of the circle. First, we need to find the radius.
Calculate the Radius The radius of a circle is half of its diameter. Since the diameter is 16 inches, the radius r is calculated as: r = 2 d iam e t er = 2 16 = 8 inches Now that we have the radius, we can calculate the area of the circle.
Calculate the Area Now, we can calculate the area A using the formula A = π r 2 and the given value of π = 3.14 :
A = π r 2 = 3.14 × ( 8 ) 2 = 3.14 × 64 = 200.96 square inches So, the area of the circle is 200.96 square inches.
Final Answer The area of the circle with a diameter of 16 inches, using π = 3.14 , is 200.96 square inches.
Examples
Imagine you're designing a circular garden and need to determine how much area it will cover to buy the right amount of soil or fencing. Knowing the diameter (or radius) and using the formula for the area of a circle, you can easily calculate the garden's area. For instance, if your garden has a diameter of 16 feet, you can calculate the area as A = π r 2 = 3.14 × ( 8 ) 2 = 200.96 square feet, helping you plan your gardening project effectively.
