How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50
-foot
radius?
To find the circumference of the circle, we use the formula:
Circumference = 2πr
Where r is the radius of the circle and π is approximately 3.14.
Substituting r = 50 feet, we get:
Circumference = 2π(50) = 100π ≈ 314.16 feet
Since the flowers are spaced 6 inches apart, we need to convert feet to inches:
314.16 feet × 12 inches/foot = 3769.92 inches
To determine how many flowers are needed, we divide the circumference by the spacing between the flowers:
3769.92 inches ÷ 6 inches/flower ≈ 628.32 flowers
Since we can't have a fraction of a flower, we round up to the nearest whole number:
628.32 ≈ 629 flowers
Therefore, we need 629 flowers to surround the circular garden with a 50-foot radius, spaced every 6 inches.
To calculate the number of flowers needed to surround a circular garden with a 50-foot radius, we need to find the perimeter of the circle and divide it by the spacing between the flowers.
The formula for the perimeter of a circle is 2πr, where r is the radius.
Perimeter = 2πr
Perimeter = 2π(50)
Perimeter = 100π feet
Now, we need to convert the perimeter to inches because the spacing between the flowers is given in inches.
1 foot = 12 inches
Perimeter in inches = (100π)(12)
Perimeter in inches ≈ 376.99 inches
Since the flowers are placed every 6 inches, we divide the perimeter (in inches) by the spacing (in inches).
Number of flowers = Perimeter in inches ÷ Spacing
Number of flowers = 376.99 ÷ 6
Number of flowers ≈ 62.83
So, approximately 62.83 flowers would be needed to surround the circular garden with a 50-foot radius, spaced every 6 inches. Since we can't have a fraction of a flower, we would round up to the nearest whole number.
Therefore, about 63 flowers would be needed.