Circle Geometry and Formulas

The video tutorial covers the concepts of circumference and area of circles. It begins with a problem involving the circumference of a hula hoop to find its radius. Next, it addresses a penguin swimming around a circular island, requiring the calculation of distance using circumference. The tutorial then moves to a sumo wrestling ring, where the area is calculated from the given circumference. Finally, it discusses a butterfly sculpture with circular dots, calculating the area needed for glass filling. Each section involves applying formulas for circumference and area, emphasizing practical problem-solving in geometry.

If the circumference of a circle is given as 86π cm, what is the radius?

• 43 cm

• 86 cm

• 21.5 cm

• 172 cm

Which formula is used to calculate the circumference of a circle when the radius is known?

• πd

• πr²

• d/2

• 2πr

A penguin swims halfway around a circular island with a diameter of 20 meters. How far does it swim?

• 10π meters

• 5π meters

• 20π meters

• 40π meters

What is the formula for the circumference of a circle using its diameter?

• πr²

• d/2

• 2πr

• πd

Given a sumo wrestling ring with a circumference of 46π meters, what is the radius?

• 11.5 meters

• 23 meters

• 46 meters

• 92 meters

How do you calculate the area of a circle when the radius is known?

• d²/4

• πd

• 2πr

• πr²

If the circumference of a circle is 4.6π meters, what is the radius?

• 2.3 meters

• 4.6 meters

• 1.15 meters

• 9.2 meters

A circular dot on a butterfly sculpture has a circumference of 24π inches. What is the radius?

• 6 inches

• 48 inches

• 24 inches

• 12 inches

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

• 48π square inches

• 72π square inches

• 24π square inches

• 144π square inches

Which formula is used to find the area of a circle?

• d²/4

• πd

• 2πr

• πr²