Question

The figure shows a planetarium’s viewing room, which is in the shape of a hemisphere. The diameter of the hemisphere is 50 feet. What is the volume of the viewing room of the planetarium? (Use 3.14 for π. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume of a sphere is .) 10,416.7 cu. ft. 16,354.2 cu. ft. 32,708.3 cu. ft. 65,416.7 cu. ft.

Answer 1

You did not include the figure, but according to the statement the viewing room of the planetarium is in the shape of a hemisphere.

A hemisphere is half a sphere.

So, the volume of a hemisphere is the half of the volume of the complete sphere.

The formula for the volume of a sphere is:

V = (4/3) π (radius)^3

Using π = 3.14 and radius = diameter / 2 = 50 feet / 2 = 25 feet.

You get:

V = (4/3) (3.14) (25 feet)^3 = 65,416.7 feet^3

Answer: 65,416.7 cu. ft.

Answer 2

32,708.3 cu. ft

Explanation:

First we find the volume of a sphere with the same dimensions

`V=(4)/(3) \pi r^(3)` is the formula for the volume of a sphere

`V=(4)/(3) \((3.14)25^(3)` substitute the radius with 25 because radius is half the diameter and use 3.14 for pie. The answer to that formula is 65,416.6

Since you're finding the volume of a hemisphere, divide the volume of the sphere in half

65,416.6/2= 32,708.3