The dome of a new building provides a panoramic view of New York. A tourists stands in the center of the dome and has a 12 degree view through one window. What is the approximate diameter of the dome if the window is 18 inches wide?
2007-11-07 14:03:09 · 4 answers · asked by Sellie 2 in Science & Mathematics ➔ Mathematics
172 inches is the diameter of the dome:
a 12 degree view means each window is 12/360 the circumference of the dome. 12/360 = 1/30 so there are 30 such windows. If each window is 18 inches, then the total circumference is 18 x 30 = 540 inches. Since C = TT x D,
D = 540 / TT = 172. 172 inches = 14 1/3 feet.
2007-11-07 14:08:28 · answer #1 · answered by davidosterberg1 6 · 0⤊ 0⤋
And by dome you mean... I assume a hemisphere?
I assume by 18 inches, you mean an arc length of 18 inches along the suface of the hemisphere.
Draw a circle. Label the center C. Open up a central angle at the center. It's a 12 degree angle. The arc intercepted along the circumference is 18 inches.
Make a proportion:
12 degrees / 18 inches = 360 degrees / x inches.
The x will be the circumference of the circle. Solve for it.
Next, use
circumference = 2*pi*r
to find the radius. Then double that to get the diameter.
Of course, this is assumning that by "dome" you mean hemisphere.
If you want the actual poblem that gives you the diameter, it's
(2*360*18)/(12*2*pi), or 540/pi inches
2007-11-07 14:06:33 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The approximation is that the sum of all window lengths is the circle's circumference. So if each window has a 12-degree view, there are 30 windows. Then, the sum of window lengths is 18*30= 540 inches or 45 feet. This equals pi*d.
2007-11-07 14:12:51 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋
12 degrees is 1/30 of the circle. The circumference is a little more than 540 inches. The diameter is 540/pi or about 172 inches.
2007-11-07 14:15:11 · answer #4 · answered by chesler.geo 2 · 0⤊ 0⤋