10-01-2020
Mathematics

contestada

A fish tank is in the shape of a rectangular prism with dimensions 36 in. x 12 in. x 12
in. The tank is 80% filled with water. A stone, roughly the shape of a sphere with a 4
in. radius, is placed in the tank. The stone sinks to the bottom.
How many cubic inches of space in the fish tank remain in the tank after the stone is
added to the tank?

Respuesta :

sqdancefan sqdancefan

11-01-2020

Answer:

about 769 cubic inches

Step-by-step explanation:

Before the stone is added, 20% of the tank volume is empty. The empty volume is ...

0.20LWH = 0.20(36 in)(12 in)² = 7.2×144 in³ = 1036.8 in³

The volume of the sphere is given by ...

V = (4/3)πr³ = (4/3)π(4 in)³ = 256π/3 in³ ≈ 268.08 in³

Then the remaining empty volume after the stone is added is ...

1036.80 in³ -268.08 in³ = 768.72 in³

The empty volume in the tank after the stone is added is about 768.72 in³.

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