a circle has a diameter of 10cm.. a PERFECT STAR is inserted inside the circle.. what will be the area that is not occupied by the star inside the circle? (d=10cm is the only given value)
2007-01-10 18:47:55 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
It's bedtime, but I want to answer one more.
I assume you mean a pentagram when you say "perfect star".
I found a formula for the area of a pentagram (ref below).
It's (5s²/4)(Tan( 3π/10 ) - Tan( π/5 )), where s is the side of the pentagon around the star.
From one of my previous answers (ref below), the relationship between s and the radius is s = 2 r cos 54°
So, for this problem, r = 5, and the area NOT occupied by the star would be:
π r² - (5 r² cos² 3π/10)(Tan( 3π/10 ) - Tan( π/5 )) = 24.315 cm²
2007-01-10 19:31:27 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
How many points on the star?
2007-01-10 19:16:25 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
I think about one inch as the normal length of the cylinder is about 6 to 7 inches.
2007-01-10 19:34:58 · answer #3 · answered by Anonymous · 0⤊ 0⤋
how many sides does a perfect star has?
2007-01-10 19:45:07 · answer #4 · answered by rishi 2 · 0⤊ 0⤋
how do you define a perfect star?
2007-01-10 18:55:02 · answer #5 · answered by Anonymous · 0⤊ 0⤋