This is the one problem keeping me from passing trig. PLEASE HELP IF YOU CAN!!
A round table can be made square by dropping the 4 leaves. If a side of the square table measures 36 inches to the nearest hundredth of a square inch, how much smaller is the area of the table when the leaves are down then when the leaves are up.
THANKS!
2006-10-09 15:04:09 · 8 answers · asked by Anonymous in Education & Reference ➔ Homework Help
First off find the diamater of the circle with the leaves up using the formula. This diamater is the same as the diagonal measurement of the square. Cut the square in half it forms a triangle, the side opposite the 90degree angle is the hypotenuse.
a^2 + b^2 = c^2
36^2 + 36^2 = c^2
2592 = c^2
c = 50.9116882454
radius = 25.4558441227
Now to get the area of the circle, use the formula PI * radius^2
Total area of circle = 2035.75203953
Now you have to find the total area of the square. This is simple, the base times itself.
36*36 = x
Total area of square = 1296
So the answer to the question: How much smaller is the are of the table when the leaves are down is
2035.75203953 - 1296 = 739.75203953 square inches
Hit me with the best answer plz :)
2006-10-09 15:33:43 · answer #1 · answered by gilafro 2 · 1⤊ 0⤋
4.326 square feet. Your table would have 9 square feet with leaves down: (3 x 3 = 9) inches converted to feet. with the leaves up and the table round, the diameter times Pi (3.141) would equal the area. The diameter is found by the pythagorian formula: a 2 + b2 = c2 3 x 3 = 9 plus 3 x 3 =9 9+9 = 18 the square root of 18 is 4.326134 4.326134 x 3.141 = 13.588386. Now subtract 9 (the "square table") from the "round table" and the difference is 4.326 square feet.
2006-10-09 15:21:05 · answer #2 · answered by londo_h_mollari 2 · 0⤊ 0⤋
2 diagonals of a square are perpendicular.
And each diagonal is equal to the diameter of the circle.
so the diameter of the circle is: 36* sqrt(2).
The area of the square is 36^2 = 1296
The area of the circle is: pi* [18 * sqrt (2)]^2= pi* 648
so the ratio is: 1296 / 648 * pi = 2 / pi
2006-10-09 15:26:54 · answer #3 · answered by hoang_hiepsi 4 · 0⤊ 0⤋
I won't tell you, but I'll give you a hint to help you on your way. The hypotenuse from 1 corner of the table to the other can be found with the pythagorus. You already have the 36 inches. That value will be the same as the diameter of the circle you are looking for.
2006-10-09 15:10:52 · answer #4 · answered by Maniac Number One 2 · 1⤊ 0⤋
This is fun.
A square that fits entirely inside a circle is called a circumscribed square. Therefore, the diagonal of the square = the diameter of the circle.
Diagonal of square = square root of (36*36) + (36*36) = approx. 50.9 inches.
Area of square = 36*36 = 1,296 sq inches
Area of circle = pi*radius-squared = 3.14*(50.9/2)-squared = 3.14*25.45*25.45 = 2033.8 sq inches
Subtract the two areas: 2033.8 - 1296
= 737.8 sq-in
2006-10-09 15:14:25 · answer #5 · answered by Tom-SJ 6 · 0⤊ 0⤋
36" is the short side of the right triangle where the hypoteneuse is the diameter (d) of the circle.
so 36² + 36² = d²
radius =d/2
area of cicle is π r²
area of square is 36²
2006-10-09 15:23:08 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Two hints ...
1. diagonal of the square = diameter of the circle.
2. difference in area will be (area of the circle) - (area of the square).
Guido
2006-10-09 15:14:43 · answer #7 · answered by Anonymous · 0⤊ 0⤋
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2016-10-19 02:57:09 · answer #8 · answered by balderas 4 · 0⤊ 0⤋