In designing a circular flower bed where the diameter of the circle is 13 feet​ long, a gardener decides it would look best to space the flowers 7 inches apart. How many flowers will be needed around the outside of the flower​ bed?

(I've tried finding the circumference and dividing it by 7.. No idea how to do this. Some sort of formula?)

Thanks! (:

you have the right idea. but you need to change feet to inches, so the units match:

13π*12/7 = 70.01

So, there will be 70 spaces between flowers. Since they are in a circle, there will be 70 flowers.

Had they been in a line, there would have been 71, since the ends would each have a flower.

Thank you so much, Steve!!

To find the number of flowers needed around the outside of the flower bed, we can use the formula for the circumference of a circle, which is C = πd or C = 2πr.

In this case, we know the diameter of the circle is 13 feet. The radius (r) of the circle is half the diameter, so r = 13/2 = 6.5 feet.

To find the circumference (C), we can substitute the value of the radius (r) into the formula C = 2πr:

C = 2π(6.5) ≈ 2π(6.5) = 13π feet.

Now, to determine the number of flowers needed, we need to find out how many 7-inch segments will fit into the circumference.

Since 1 foot is equal to 12 inches, we can convert the circumference (in feet) to inches by multiplying it by 12:

C_in_inches = 13π × 12 = 156π inches.

Next, we can divide the circumference in inches by the spacing between the flowers (7 inches) to find the number of flowers needed:

Number_of_flowers = C_in_inches / Spacing_between_flowers = 156π inches / 7 inches ≈ 22.29π.

Since we can't have a fractional number of flowers, we need to round up to the nearest whole number of flowers. Therefore, we can conclude that approximately 23 flowers will be needed around the outside of the flower bed.

Please note that π is an irrational number approximately equal to 3.14159, and we have used its approximate value in our calculations.