Calculating the Area of the Tabletop

Oct 13, 2025 by miodeya.com 23 views

Introduction

When it comes to calculating the area of a circular tabletop, we need to use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius of the circle. In this problem, we are given that the radius of the tabletop is 24 inches, and we are asked to find the area of the tabletop to the nearest square inch. We will use the value of π as 3.14.

Calculating the Area of the Tabletop

To calculate the area of the tabletop, we need to plug in the value of the radius into the formula A = πr^2. We will use the value of π as 3.14 and the radius as 24 inches.

A = πr^2 A = 3.14(24)^2 A = 3.14(576) A = 1809.44

Rounding the Answer to the Nearest Square Inch

Since we are asked to find the area of the tabletop to the nearest square inch, we need to round the answer to the nearest whole number. The answer is 1809.44, which rounds to 1809.

Conclusion

In conclusion, the area of the tabletop is 1809 square inches to the nearest square inch.

Comparison of Options

Let's compare our answer with the options given:

A. 75 in. ^2 B. 151 in. ^2 C. 1809 in. ^2 D. 7235 in.

Our answer, 1809 in. ^2, matches option C.

Final Answer

The final answer is C. 1809 in. ^2.

Discussion

This problem is a basic application of the formula for the area of a circle. It requires the student to plug in the value of the radius into the formula and calculate the area. The student must also round the answer to the nearest whole number.

Tips and Tricks

Make sure to use the correct value of π, which is 3.14.
Plug in the value of the radius into the formula A = πr^2.
Calculate the area by multiplying π by the square of the radius.
Round the answer to the nearest whole number.

Common Mistakes

Using the wrong value of π.
Not plugging in the value of the radius into the formula.
Not calculating the area correctly.
Not rounding the answer to the nearest whole number.

Real-World Applications

This problem has real-world applications in various fields such as architecture, engineering, and design. For example, architects and engineers use the formula for the area of a circle to calculate the area of circular structures such as bridges, tunnels, and buildings.

Practice Problems

A circular table has a radius of 15 inches. What is the area of the table, to the nearest square inch? Use 3.14 for π.
A circular garden has a radius of 20 feet. What is the area of the garden, to the nearest square foot? Use 3.14 for π.
A circular pool has a radius of 30 feet. What is the area of the pool, to the nearest square foot? Use 3.14 for π.

Solutions to Practice Problems

A = πr^2 A = 3.14(15)^2 A = 3.14(225) A = 706.5 Rounded to the nearest square inch, the answer is 706 in. ^2.
A = πr^2 A = 3.14(20)^2 A = 3.14(400) A = 1256 Rounded to the nearest square foot, the answer is 1256 ft. ^2.
A = πr^2 A = 3.14(30)^2 A = 3.14(900) A = 2826 Rounded to the nearest square foot, the answer is 2826 ft. ^2.

Q&A: Calculating the Area of a Circular Tabletop

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

Q: What is the value of π used in this problem?

A: The value of π used in this problem is 3.14.

Q: How do I calculate the area of the tabletop?

A: To calculate the area of the tabletop, plug in the value of the radius into the formula A = πr^2. Multiply π by the square of the radius to get the area.

Q: What is the radius of the tabletop in this problem?

A: The radius of the tabletop in this problem is 24 inches.

Q: What is the area of the tabletop, to the nearest square inch?

A: The area of the tabletop is 1809 square inches to the nearest square inch.

Q: How do I round the answer to the nearest square inch?

A: To round the answer to the nearest square inch, look at the decimal part of the answer. If the decimal part is less than 0.5, round down. If the decimal part is 0.5 or greater, round up.

Q: What are some common mistakes to avoid when calculating the area of a circle?

A: Some common mistakes to avoid when calculating the area of a circle include using the wrong value of π, not plugging in the value of the radius into the formula, not calculating the area correctly, and not rounding the answer to the nearest whole number.

Q: What are some real-world applications of the formula for the area of a circle?

A: The formula for the area of a circle has real-world applications in various fields such as architecture, engineering, and design. For example, architects and engineers use the formula to calculate the area of circular structures such as bridges, tunnels, and buildings.

Q: Can you provide some practice problems for calculating the area of a circle?

A: Here are some practice problems for calculating the area of a circle:

A circular table has a radius of 15 inches. What is the area of the table, to the nearest square inch? Use 3.14 for π.
A circular garden has a radius of 20 feet. What is the area of the garden, to the nearest square foot? Use 3.14 for π.
A circular pool has a radius of 30 feet. What is the area of the pool, to the nearest square foot? Use 3.14 for π.

Q: Can you provide the solutions to the practice problems?

A: Here are the solutions to the practice problems:

A = πr^2 A = 3.14(15)^2 A = 3.14(225) A = 706.5 Rounded to the nearest square inch, the answer is 706 in. ^2.
A = πr^2 A = 3.14(20)^2 A = 3.14(400) A = 1256 Rounded to the nearest square foot, the answer is 1256 ft. ^2.
A = πr^2 A = 3.14(30)^2 A = 3.14(900) A = 2826 Rounded to the nearest square foot, the answer is 2826 ft. ^2.

Q: What are some tips for calculating the area of a circle?

A: Some tips for calculating the area of a circle include:

Make sure to use the correct value of π.
Plug in the value of the radius into the formula A = πr^2.
Calculate the area by multiplying π by the square of the radius.
Round the answer to the nearest whole number.

Q: What are some common mistakes to avoid when calculating the area of a circle?

A: Some common mistakes to avoid when calculating the area of a circle include:

Using the wrong value of π.
Not plugging in the value of the radius into the formula.
Not calculating the area correctly.
Not rounding the answer to the nearest whole number.