Final answer:
The question is about calculating the area of an outfield, which implies using the area formula for circles, A = πr². When a radius is given, the area can be calculated and rounded according to the significant figures of the radius measurement.
Step-by-step explanation:
The size of the outfield is a question often addressed in geometry, a branch of mathematics concerned with the properties and relations of points, lines, surfaces, and solids. To elucidate the concept of measurement and area calculation, let's take the formula for the area of a circle, which is A = πr². In this equation, π (pi) represents approximately 3.14159, the ratio of a circle's circumference to its diameter, and r is the radius of the circle. If we calculate the area with a radius of 1.2 meters, the area would be A = π(1.2 m)². When using a calculator with an eight-digit output, you'd get A = 4.5238934 m². However, due to the significant figures rule, we would round this to A = 4.5 m², due to the radius having only two significant figures.
Understanding how to manipulate and approximate mathematical expressions is essential, especially when you don't have a calculator. For instance, 10³π ≈ √10 demonstrates how we can use approximation (≈) to simplify expressions. Turning a circle into a square is a helpful trick to make sense of geometric measures, such as perimeter and area. Just remember that with squares, if each side length is a, then the perimeter is 4a and the area is a².
In the physical sciences, such as physics, symbols and their dimensions are often used, representing the physical quantity they measure. For example, the radius (r) of a cylinder and the height (h) both have dimensions of length [L], while the area (A) is expressed in square units [L²], and volume (V) in cubic units [L³]. This is crucial when calculating areas and volumes, ensuring we use the correct units for our calculations.