What is the area of a circular reservoir with a diameter of 411 feet, expressed in square feet?

What is the area of a circular reservoir with a diameter of 411 feet, expressed in square feet?

• A. 130,000 ft²
• B. 133,000 ft²
• C. 140,000 ft²
• D. 150,000 ft²

Answer: (B)

To find the area of a circular reservoir, you can use the formula for the area of a circle, which is \( A = \pi r^2 \), where \( r \) is the radius of the circle. Given that the diameter of the reservoir is 411 feet, the radius would be half of the diameter. Therefore, the radius is: \[ r = \frac{diameter}{2} = \frac{411}{2} = 205.5 \text{ feet} \] Now plug the radius into the area formula: \[ A = \pi (205.5)^2 \] Calculating \( (205.5)^2 \) gives approximately \( 42220.25 \) square feet. When you multiply this by \( \pi \) (approximately 3.14159), the area becomes: \[ A \approx 3.14159 \times 42220.25 \approx 132,695.84 \text{ square feet} \] Rounding this result gives approximately 133,000 square feet. Selecting the answer that closely matches this calculation confirms that the area of the circular reservoir is best expressed as 133,000 square feet. This is

To find the area of a circular reservoir, you can use the formula for the area of a circle, which is ( A = \pi r^2 ), where ( r ) is the radius of the circle. Given that the diameter of the reservoir is 411 feet, the radius would be half of the diameter. Therefore, the radius is:

[

r = \frac{diameter}{2} = \frac{411}{2} = 205.5 \text{ feet}

]

Now plug the radius into the area formula:

[

A = \pi (205.5)^2

]

Calculating ( (205.5)^2 ) gives approximately ( 42220.25 ) square feet. When you multiply this by ( \pi ) (approximately 3.14159), the area becomes:

[

A \approx 3.14159 \times 42220.25 \approx 132,695.84 \text{ square feet}

]

Rounding this result gives approximately 133,000 square feet. Selecting the answer that closely matches this calculation confirms that the area of the circular reservoir is best expressed as 133,000 square feet.

This is