Shell Game 1

Geometry Level 3

A cubic vault with dimensions 1 0 ′ × 1 0 ′ × 1 0 ′ 10' \times 10' \times 10' has steel walls, ceiling and floor 6 inches thick. What is the volum of the stell to the nearest 0.1 cubic feet?


The answer is 271.

Guiseppi Butel by Guiseppi Butel , 90, Canada

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2 solutions

Guiseppi Butel
Dec 2, 2015

If you subtract the 2 walls from 10' you get the dimensions of the empty space inside the vault to be 9' x 9' x 9'. The volume of this space is 729 cu.ft. Subtract this from the volume of the whole cube and you get 271 cu.ft. for the volume of the steel "shell",

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Marvin Kalngan
May 3, 2020

The volume of the steel is equal to the volume of the bigger cube minus the volume of the inner cube. The side length of the inner cube is 10 feet minus 6 inches on one side and minus 6 inches on the other side. So the side length of the inner cube is 10 feet - 0.5 feet - 0.5 feet = 9 feet.

volume of steel = 1 0 3 − 9 3 = 271 cubic feet \text{volume of steel}=10^3-9^3=\boxed{\text{271 cubic feet}}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Why are the units cubic inches?

Guiseppi Butel - 3 months, 2 weeks ago

Thank you. I edited my answer to cubic feet.

Marvin Kalngan - 3 months, 2 weeks ago

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