Geometry
posted by Tristan on .
A circular flower bed is sectioned off. The arc intercepted by the 120 degree central angle is to be bordered with marigolds. The garden has a diameter of 63 inches. Circumference = Pi * diameter, Pi = 22/7. If you plant the marigolds about eight inches apart what is the least number you must buy?

The radius of the circle is given by
2*pi/3 * r = 63
r = 30
So, the area of the 1/3 of the flower bed to be planted is
pi/3 * r^2 = pi/3 * 900 = 943 sq in.
If the marigolds are planted in a rectangular grid, that allocates 64 sq in per flower, so you'd need about
943/64 = 15 marigolds.
Of course, an 8" square grid means that diagonally opposite flowers are about 11.2" apart. If you plant them in a triangular lattice of side 8", then you'd have somewhere 20 around flowers, depending on how they were arranged