A circular swimming pool has a diameter of 30 feet and is centered in a grass region measuring 45 ft by 70 ft. a. Find the perimeter (circumference) of the pool. b. You want to fence around the circular pool. Fencing costs $3.99/ft. How much will it cost to fence the pool? c. Find the area of the grass. Hint: Draw a picture
The Correct Answer and Explanation is:
Correct Answers:
a. Perimeter (Circumference) of the Pool:
Circumference = π × diameter
= 3.14 × 30 ft
= 94.2 feet
b. Cost to Fence the Pool:
Cost = Circumference × Cost per foot
= 94.2 ft × $3.99/ft
= $375.86
c. Area of the Grass:
Step 1: Find area of the rectangular region.
Area = length × width
= 70 ft × 45 ft
= 3,150 square feet
Step 2: Find area of the circular pool.
Area = π × (radius)²
Radius = diameter ÷ 2 = 30 ÷ 2 = 15 ft
Area = 3.14 × (15)²
= 3.14 × 225
= 706.5 square feet
Step 3: Subtract pool area from total area to get grass area.
Grass area = 3,150 − 706.5 = 2,443.5 square feet
Explanation:
The problem involves a circular pool within a rectangular grassy area. To determine the pool’s perimeter, use the formula for the circumference of a circle: π times the diameter. Given the diameter of 30 feet, multiplying by the approximate value of π (3.14) gives 94.2 feet. This represents the total length around the edge of the pool.
To calculate fencing cost, multiply this perimeter by the price per foot of fencing. At $3.99 per foot, multiplying 94.2 feet by this rate results in $375.86. This represents the total expense required to encircle the pool with a fence.
For the grass area, the first step is to determine the area of the entire rectangular region. The product of its length and width (70 feet by 45 feet) equals 3,150 square feet. Next, find the area of the pool using the formula for the area of a circle, π times the radius squared. The radius is half the diameter, or 15 feet. Squaring the radius and multiplying by 3.14 yields 706.5 square feet for the pool area.
Finally, to find the grassy area, subtract the circular pool’s area from the rectangle’s area. This subtraction gives 2,443.5 square feet. This remaining space represents the grassy portion around the pool, which might be used for walking paths, seating, or landscaping.
