Circle Area and Radius Concepts

In this lesson, Mr. Hul covers the area of a circle, starting with classwork exercises on finding the radius and area of circles and rectangles. An exploratory challenge demonstrates a visual method to approximate the area of a circle. Real-world problems, such as calculating the area covered by a sprinkler and determining waste when cutting a circular table from a square, are solved. The lesson concludes with exercises to reinforce the concepts learned.

What is the formula to find the radius of a circle if its circumference is given?

• C = 2πr

• C = πd

• r = C/π

• r = C/2π

Which of the following is a method to find the area of a rectangle?

• Area = 2πr

• Area = ½ × base × height

• Area = πr²

• Area = length × width

If the area of a rectangle is 27 cm² and the width is 3 cm, what is the length?

• 3 cm

• 6 cm

• 9 cm

• 12 cm

How can the area of a circle be approximated using a rectangle?

• By measuring the diameter and multiplying by π

• By cutting the circle into 16 equal pieces and rearranging them

• By counting the number of squares inside the circle

• By using the formula πr²

What is the approximate area of a circle with a radius of 10 cm using the formula πr²?

• 100 cm²

• 314 cm²

• 628 cm²

• 157 cm²

How many squares are used to cover 1/4 of the circle in the approximation method?

• 79 squares

• 100 squares

• 314 squares

• 36 squares

What is the radius of the circular region covered by a sprinkler if the distance is 12 feet?

• 12 feet

• 18 feet

• 24 feet

• 6 feet

If a circular table is cut from a square piece of wood with a radius of 3 feet, what is the area of the waste?

• 8 ft²

• 28 ft²

• 36 ft²

• 9 ft²

What is the exact area of a circle with a radius of 2 cm?

• 16π cm²

• 2π cm²

• 8π cm²

• 4π cm²

Who is correct about the area of a circle with a diameter of 20 cm, Joan or Melinda?

• Neither is correct

• Joan, because she used the diameter

• Melinda, because she used the radius

• Both are correct