Exploring the Effects of Radius Changes on Circle Area

The video tutorial explores how the circumference and area of a circle change as the radius changes, particularly when the radius is doubled. It explains that the circumference is directly proportional to the radius, while the area is proportional to the square of the radius. The video uses algebraic expressions to demonstrate these relationships and encourages viewers to experiment with different values to understand the concepts better.

What happens to the circumference of a circle when its radius is doubled?

• It remains the same

• It quadruples

• It halves

• It doubles

If the radius of a circle is increased from X to 2X, what is the new circumference?

• πX

• 2πX

• 4πX

• 8πX

What is the circumference of a circle with radius X?

• 4πX

• πX

• πX²

• 2πX

How does the area of a circle change when the radius is doubled?

• Triples

• Increases fourfold

• Remains unchanged

• Doubles

What is the area of a circle with radius 2X?

• 4πX²

• 2πX²

• 8πX²

• πX²

What formula is used to calculate the area of a circle?

• 2πr

• πr²

• 2πr²

• πr

Why does the area of a circle increase by a factor of four when the radius is doubled?

• Area is proportional to the square of the radius

• Area is proportional to the radius

• Area is inversely proportional to the radius

• Area is unrelated to the radius

If the radius of a circle is tripled, by what factor does the area increase?

• Six

• Twelve

• Three

• Nine

What is the relationship between the radius and the circumference of a circle?

• No relationship

• Squared relationship

• Inversely proportional

• Directly proportional

If the radius of a circle is quadrupled, by what factor does the area increase?

• Sixteen

• Four

• Eight

• Twelve