Area of Circles

Front

What is the formula for the area of a circle?

Back

The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius.

Front

What does π (pi) represent in the context of circles?

Back

π (pi) is a mathematical constant approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.

Front

If the radius of a circle is 5 cm, what is its area?

Back

Using the formula A = πr², the area is A = 3.14 * (5)² = 78.5 cm².

Front

What is the area of a circle with a diameter of 10 cm?

Back

First, find the radius (r = diameter/2 = 5 cm). Then, A = πr² = 3.14 * (5)² = 78.5 cm².

Front

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

Back

You can rearrange the area formula: r = √(A/π). For example, if A = 78.5 cm², then r = √(78.5/3.14) = 5 cm.

Front

What is the area of a semicircle with a radius of 4 cm?

Back

The area of a semicircle is half the area of a circle: A = (1/2) * πr² = (1/2) * 3.14 * (4)² = 25.12 cm².

Front

What is the area of a circle with a radius of 10 m?

Back

Using the formula A = πr², the area is A = 3.14 * (10)² = 314 m².

Front

If the area of a circle is 50.24 cm², what is the radius?

Back

Using the formula r = √(A/π), r = √(50.24/3.14) ≈ 4 cm.

Front

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

Back

The diameter is twice the radius: diameter = 2 * radius.

Front

How does changing the radius affect the area of a circle?

Back

The area increases with the square of the radius; if the radius doubles, the area increases by a factor of four.