Question

A whispering gallery, often elliptical in shape, has acoustic properties such that a whisper made at one point can be

heard at other distant points. A science museum is designing a new exhibit hall that will illustrate a whispering gallery.
The hall will be 110 ft in length with the ceiling 40 ft high at the center. How far are the foci from the center of
the ellipse?

Answer 1

The distance from the center of the ellipse to each focus is 51.73 ft.

Step-by-step explanation:

The foci of an elliptical whispering gallery can be found using the formula:

c = √(a^2 - b^2)

where:

• c is the distance from the center of the ellipse to each focus
• a is the semi-major axis of the ellipse, which is half the length of the ellipsoid (110 ft/2 = 55 ft)
• b is the semi-minor axis of the ellipse, which is half the height of the ellipsoid (40 ft/2 = 20 ft)

Substituting the given values into the formula:

c = √((55 ft)2 - (20 ft)2)

c = √((3025 ft2 - 400 ft2)

c = √2675 ft2

c = 51.73 ft (rounded to two decimal places)