Homework Help: Geometry

Posted by Tristan on Monday, November 28, 2011 at 9:19am.

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?

Geometry - Steve, Monday, November 28, 2011 at 10:43am
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

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