Understanding Circles and Sectors

This video tutorial covers the calculation of the area of circles and sectors. It begins with an introduction to the concepts of circles and sectors, followed by detailed examples of calculating the area of a circle. The tutorial then explains how to calculate the area of a sector using a formula and provides examples. It also introduces a proportional method for solving area problems and concludes with application problems involving circle and sector areas.

What is a sector in a circle often compared to?

• A slice of pizza

• A piece of pie

• A wedge of cheese

• A slice of cake

What is the formula for the area of a circle?

• 2πr

• πr²

• πd

• πr

How do you calculate the area of a sector?

• Measure of the arc divided by 360, multiplied by πr²

• Measure of the arc multiplied by 360, divided by πr²

• Measure of the arc divided by πr², multiplied by 360

• Measure of the arc multiplied by πr², divided by 360

If a sector has a central angle of 120°, what fraction of the circle does it represent?

• 1/3

• 1/4

• 1/6

• 1/2

What method is used to find the area of a circle when given the area of a sector?

• Subtraction method

• Proportion method

• Addition method

• Division method

In a proportion problem, what is the first step after setting up the equation?

• Divide the fractions

• Add the fractions

• Multiply the fractions

• Cross-multiply

How can you find the radius of a circle if you know the area?

• Multiply the area by π

• Add π to the area

• Divide the area by π and take the square root

• Subtract π from the area

If a pizza has a diameter of 20 inches, what is its radius?

• 20 inches

• 15 inches

• 10 inches

• 5 inches

What is the area of a pizza slice with a central angle of 45° and a radius of 12 inches?

• 72π square inches

• 54π square inches

• 18π square inches

• 36π square inches

If a pizza slice has a central angle of 10°, what fraction of the pizza does it represent?

• 1/18

• 1/24

• 1/36

• 1/72