A land scape is preparing a circular flowerbed. The bed has a 12-foot diameter. He will need 13 plants per square yard. How many plants should he buy?
Thank you.
well, the area is πr^2 = 4π yd^2
a first approximation is thus 4π*13
To find out how many plants the landscaper should buy, we need to calculate the area of the circular flowerbed and then convert it to square yards. Here are the steps to find the answer:
1. The diameter of the circular flowerbed is given as 12 feet. We can use this information to find the radius (r) of the flowerbed, which is half the diameter. So, the radius is 12 feet divided by 2, which equals 6 feet.
2. The area of a circle can be calculated using the formula: A = πr^2, where A represents the area and π is a mathematical constant approximately equal to 3.14.
3. Plugging in the value of the radius, we can find the area of the circular flowerbed: A = 3.14 x (6 feet)^2 = 3.14 x 36 square feet.
4. To convert the area from square feet to square yards, we need to know that 1 yard is equal to 3 feet. Therefore, 1 square yard is equal to 3 feet x 3 feet = 9 square feet.
5. Dividing the area of the circular flowerbed in square feet by the conversion factor of 9 square feet per square yard, we can find the area in square yards: (3.14 x 36 square feet) ÷ 9 square feet per square yard = 12.57 square yards.
6. The landscaper requires 13 plants per square yard, so to determine the number of plants needed, we can multiply the area in square yards by 13: 12.57 square yards x 13 plants per square yard = 163.41 plants.
Since it is not possible to buy fractional plants, the landscaper should round up to the nearest whole number. Therefore, the landscaper should buy 164 plants.
I hope this explanation helps you understand how to calculate the number of plants needed for a circular flowerbed with a given diameter.