Podcast
Questions and Answers
Calculate the area of a circle with a radius of 5 units.
Calculate the area of a circle with a radius of 5 units.
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. Substituting the given radius, A = π*5^2 = 25π square units.
If a circle has an area of 36π square units, what is its radius?
If a circle has an area of 36π square units, what is its radius?
To find the radius of the circle, we use the formula A = πr^2 and solve for r. Given A = 36π, we have 36π = πr^2. Dividing both sides by π and taking the square root gives us the radius r = √36 = 6 units.
Explain how the area of a circle changes when its radius is doubled.
Explain how the area of a circle changes when its radius is doubled.
When the radius of a circle is doubled, the area increases by a factor of 4. This is because the area of a circle is proportional to the square of its radius. So if the radius is doubled, the area becomes 2^2 = 4 times larger.
Study Notes
Area of a Circle
- To calculate the area of a circle, you need to know its radius.
- The formula to calculate the area of a circle is: Area = π × radius²
- If the radius is 5 units, the area of the circle would be: Area = π × 5² = 25π square units
Radius of a Circle with a Given Area
- If the area of a circle is 36π square units, you can find its radius by rearranging the formula: radius = √(Area / π)
- Plugging in the given area, you get: radius = √(36π / π) = 6 units
Effect of Doubling the Radius
- When the radius of a circle is doubled, its area increases by a factor of 4 (since the radius is squared in the area formula).
- For example, if the original radius is 5 units, the area would be 25π square units. If the radius is doubled to 10 units, the area would become 100π square units.
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Description
Test your understanding of circle area calculations and the relationship between radius and area. This quiz covers finding the area of a circle with a given radius, determining the radius from the area, and understanding how the area changes when the radius is doubled.
