The shape that has an area formula of 2πr² is a sphere. The formula 2πr² represents the surface area of a sphere. Here’s a brief explanation:
A sphere is a perfectly round three-dimensional shape where every point on its surface is equidistant from its center. The surface area of a sphere is calculated using the formula:
Surface Area = 4πr²
However, the formula 2πr² is often used in specific contexts, such as calculating the surface area of a hemisphere (half of a sphere). The surface area of a hemisphere is given by:
Surface Area of Hemisphere = 2πr²
This formula accounts for the curved surface area of the hemisphere. If you need to include the flat circular base, the total surface area would be:
Total Surface Area of Hemisphere = 2πr² + πr² = 3πr²
So, when you see the formula 2πr², it typically refers to the surface area of a hemisphere.