Circle Geometry and Area Problems

Mrs. Groovy Groves explains the formula for the area of a circle, pi r squared, and its derivation. The lesson includes a detailed explanation of why r squared gives the area, using the concept of dividing a circle into smaller parts. Practical examples and practice problems are provided to reinforce understanding. The lesson concludes with a summary and final remarks.

What is the formula for the area of a circle?

• pi r squared

• 2 pi r

• pi d

• r squared

How can a circle be divided to help derive the area formula?

• Into hexagons

• Into smaller pieces resembling a rectangle

• Into triangles

• Into squares

What is the correct order of operations when using the formula pi r squared?

• Square pi, then multiply by the radius

• Multiply pi by r, then square the result

• Square the radius, then multiply by pi

• Multiply pi by the diameter

If the diameter of a circle is 6 inches, what is the radius?

• 6 inches

• 3 inches

• 12 inches

• 1.5 inches

What is the area of a circle with a radius of 4 inches?

• 25 pi square inches

• 50.27 square inches

• 8 pi square inches

• 16 pi square inches

If a circle has a diameter of 2 meters, what is its area approximately?

• 3.14 square meters

• 6.28 square meters

• 12.57 square meters

• 1.57 square meters

What is the area of a circle with a radius of 5 inches?

• 50 pi square inches

• 31.42 square inches

• 78.54 square inches

• 25 pi square inches

If the diameter of a circle is 4 inches, what is the radius?

• 1 inch

• 8 inches

• 4 inches

• 2 inches

What is the area of a circle with a radius of 6 centimeters?

• 36 pi square centimeters

• 113.1 square centimeters

• 72 pi square centimeters

• 18 pi square centimeters

If a circle has a diameter of 9 inches, what is its radius?

• 9 inches

• 3 inches

• 4.5 inches

• 18 inches