A circular table top has a radius of 24 inches. What is the area of the table top, to the nearest square inch? Use 3.14 for [tex]$\pi$[/tex].
Answer (1)
Use the formula for the area of a circle: A re a = π r 2 .
Substitute the given values: A re a = 3.14 × ( 24 ) 2 .
Calculate the area: A re a = 1808.64 .
Round the result to the nearest square inch: 1809 in . 2 .
Explanation
Problem Analysis We are given a circular table top with a radius of 24 inches. We need to find the area of the table top to the nearest square inch, using 3.14 as the value for π .
Area Formula The formula for the area of a circle is given by: A re a = π r 2 where r is the radius of the circle.
Calculate the Area We are given that the radius r = 24 inches and π = 3.14 . Substituting these values into the formula, we get: A re a = 3.14 × ( 24 ) 2 A re a = 3.14 × 576 A re a = 1808.64
Round to Nearest Square Inch We need to round the area to the nearest square inch. Since the decimal part is 0.64, which is greater than 0.5, we round up to the nearest whole number. A re a ≈ 1809 Therefore, the area of the table top is approximately 1809 square inches.
Final Answer The area of the table top, to the nearest square inch, is 1809 square inches.
Examples
Understanding the area of a circle is useful in many real-life situations. For example, if you're planning to build a circular patio in your backyard, you'll need to calculate the area to determine how much paving material to purchase. Similarly, if you're baking a circular pizza and want to know how much dough you need, calculating the area will help you estimate the required amount. Knowing how to calculate the area of a circle allows you to efficiently plan and execute various projects and tasks.
