A Circular pool has diameter of 24 feet what’s the area of the cover – 452.16 square feet – 75.36 square feet – 150.72 square feet – 1,808.64 square feet
The Correct Answer and Explanation is:
To determine the area of a circular pool cover, the formula for the area of a circle is used:Area=πr2\text{Area} = \pi r^2Area=πr2
The diameter of the pool is 24 feet. The radius is half of the diameter:r=242=12 feetr = \frac{24}{2} = 12 \text{ feet}r=224=12 feet
Substituting into the formula:Area=π×122=π×144\text{Area} = \pi \times 12^2 = \pi \times 144Area=π×122=π×144
Using the approximation π≈3.1416\pi \approx 3.1416π≈3.1416:Area≈3.1416×144=452.3904 square feet\text{Area} \approx 3.1416 \times 144 = 452.3904 \text{ square feet}Area≈3.1416×144=452.3904 square feet
Rounding this to two decimal places gives approximately 452.16 square feet.
The correct answer is: 452.16 square feet
Explanation:
The concept of a circle’s area originates from geometry. The formula πr2\pi r^2πr2 calculates how much two-dimensional space lies within the boundary of a circle. This calculation involves squaring the radius, a linear measurement, which transforms it into an area measurement.
When a pool has a circular shape, any cover meant to fit it perfectly must match its area. The diameter is given directly, making it necessary to first find the radius, as the area formula depends on that value. Halving the diameter gives the radius, which then gets squared. This squaring is a crucial step, as it reflects how both the length and width contribute to the area in square units.
Multiplying the squared radius by π, the mathematical constant representing the ratio of a circle’s circumference to its diameter, completes the formula. The result provides the exact square footage needed to manufacture or size a pool cover that completely shelters the water’s surface. This ensures efficiency in material use and proper fitting.
Choosing the answer among the given options requires calculating or approximating accurately. Among the choices, only 452.16 square feet matches the correct area based on mathematical computation.
