A landscaper is preparing a circular flowerbed. The bed has a 12-foot diameter. He will need 13plants per square yard. How many plants should he buy?

radius = 6 feet = 2 yards

A = pi * r^2

A = 3.14 * 2^2

A = 12.56 sq. yards

12.56 * 13 = 163.28 = 163 plants

thank you Ms Sue

You're welcome, Danielle.

Well, the landscaper is in for some serious plant math! To begin, let's find the area of the circular flowerbed. Since the diameter is 12 feet, the radius would be half of that, which is 6 feet. Now, using the formula for the area of a circle (A = πr^2), we can calculate that the flowerbed has an area of around 113.1 square feet.

But wait, we need the area in square yards since the planting density is given in plants per square yard. Since 1 yard is equal to 3 feet, there are 9 square feet in a square yard. Dividing the area of the flowerbed (113.1 square feet) by 9, we get approximately 12.57 square yards.

According to the given planting density of 13 plants per square yard, the landscaper should buy around 12.57 x 13 = 163.41 plants. However, since you can't buy a fraction of a plant, the landscaper should buy 164 plants. I hope he has a wheelbarrow big enough to carry all those plants!

To calculate the number of plants the landscaper should buy, we need to find the area of the circular flowerbed and then convert that area into square yards.

1. To find the area of a circle, we can use the formula: A = π * r^2, where A is the area and r is the radius. Since we are given the diameter (12 feet), we can find the radius by dividing it by 2: r = 12 feet / 2 = 6 feet.

2. Now, we can calculate the area of the circle: A = π * 6^2 = π * 36 ≈ 113.1 square feet.

3. To convert the area from square feet to square yards, we divide by the conversion factor: 1 square yard = 9 square feet. So, the area in square yards is 113.1 square feet / 9 = 12.57 square yards (rounded to two decimal places).

4. Finally, we can find the number of plants the landscaper needs to buy by multiplying the area in square yards by the plant density: 12.57 square yards * 13 plants per square yard = 163.41 plants.

Therefore, the landscaper should buy approximately 163 plants to cover the circular flowerbed.