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.

Question

Mathematics

Dorian Horne

11 July, 07:16

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.

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Answers (1)

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Kenny Lam · 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.