Understanding Circle Areas

The video tutorial explains how to find the area of one of seven small circles that are tangent to a larger circle. Given the area of the large circle, the tutorial demonstrates how to calculate its radius and subsequently determine the diameter and radius of the smaller circles. Finally, it shows how to compute the area of one small circle using its radius.

What is the area of the large circle given in the problem?

• 48π

• 36π

• 24π

• 18π

How do you calculate the radius of a circle if you know its area?

• Multiply the area by π and take the square root

• Multiply the area by 2π and take the square root

• Divide the area by π and take the square root

• Divide the area by 2π and take the square root

What is the radius of the large circle?

• 12

• 9

• 6

• 3

How is the diameter of the large circle related to the diameters of the small circles?

• The diameter of the large circle is twice the diameter of a small circle

• The diameter of the large circle is three times the diameter of a small circle

• The diameter of the large circle is half the diameter of a small circle

• The diameter of the large circle is equal to the diameter of a small circle

What is the diameter of one of the small circles?

• 2

• 6

• 4

• 8

What is the radius of one of the small circles?

• 2

• 4

• 1

• 3

How do you calculate the area of a circle given its radius?

• Multiply the radius squared by 2π

• Multiply the radius by 2π

• Multiply the radius squared by π

• Multiply the radius by π

What is the area of one of the small circles?

• 2π

• 5π

• 3π

• 4π

If the radius of a small circle is doubled, what happens to its area?

• The area is halved

• The area remains the same

• The area is quadrupled

• The area is doubled

If the area of a circle is 36π, what is its diameter?

• 12

• 18

• 24

• 6