Exploring Area and Circumference of Circles

Mr. Allen introduces the concepts of area and circumference of circles. He demonstrates how to calculate the area of a circle using its diameter and radius, and how to find the circumference using the radius. The tutorial also covers more challenging problems, such as calculating the area from a given circumference and finding the circumference from a given area. The video emphasizes keeping results in terms of Pi for exactness and provides step-by-step solutions to enhance understanding.

What is the area of a circle with a diameter of 12 inches?

• 72π square inches

• 36π square inches

• 24π square inches

• 18π square inches

What is the formula to find the area of a circle?

• πr²

• 2πr

• πd

• 2πd

If the radius of a circle is 8 meters, what is its circumference using the formula 2πr?

• 64π meters

• 8π meters

• 32π meters

• 16π meters

Which formula can also be used to calculate the circumference if the diameter is known?

• diameter / π

• π * diameter

• 2 * diameter

• 2π * diameter

Given the circumference of a circle as 18π, what is the radius?

• 18 units

• 4.5 units

• 9 units

• 36 units

What is the area of a circle if the radius derived from the circumference is 9 units?

• 81π square units

• 18π square units

• 36π square units

• 72π square units

How do you calculate the radius if you know the area of the circle is 49π square inches?

• 14 inches

• 21 inches

• 49 inches

• 7 inches

What is the circumference of a circle with a radius of 7 inches?

• 14π inches

• 28π inches

• 7π inches

• 49π inches

Which operation is used to solve for the radius when you know the area of the circle?

• Multiplication

• Square

• Square root

• Division

If the area of a circle is given as 36π square units, what is the radius?

• 6 units

• 12 units

• 18 units

• 3 units