Finding Radius and Area of Circles

The video tutorial explains how to determine the radius of a circle given the area of a sector. It involves setting up a proportion using the known sector area and angle, then solving for the radius using cross multiplication. Once the radius is found, the tutorial demonstrates how to calculate the entire circle's area using the radius and the formula for the area of a circle.

What is the first step in finding the radius of a circle sector when given its area?

• Set up a proportion using the given area.

• Calculate the circumference of the circle.

• Find the diameter of the circle.

• Directly solve for the radius using the area formula.

In the proportion setup, what is typically unknown?

• The area of the entire circle.

• The angle of the sector.

• The circumference of the circle.

• The radius of the circle.

What mathematical operation is used to solve the proportion for the radius?

• Division

• Addition

• Subtraction

• Cross-multiplication

After cross-multiplying, what is the next step in solving for the radius?

• Add the results.

• Divide both sides by the coefficient of R squared.

• Multiply both sides by the angle.

• Subtract the smaller value from the larger one.

What is the approximate radius of the circle when the area of the sector is given as 35 meters squared?

• 9.5 meters

• 12.5 meters

• 10.2 meters

• 11.0 meters

What formula is used to find the area of the entire circle once the radius is known?

• πd

• πr^2

• 2πr

• 2πr^2

What value is used for π in the calculations for approximate answers?

• 3.14159

• 3.14

• 3.142

• 3.141

What is the approximate area of the entire circle when the radius is 10.2 meters?

• 320.00 meters squared

• 310.00 meters squared

• 314.16 meters squared

• 315.26 meters squared