Question

Which expression represents the volume, in cubic units, of empty space in the cube? four-thirdsπ(4.53) – (4.5)3 (9)3 – four-thirdsπ(4.52) four-thirdsπ(4.53) – (9)3 (9)3 – four-thirdsπ(4.53)

Answer 1

The expression that represents the volume of the empty space is  9³ -  4 / 3 π(4.5)³ cubic units.

How to find the expression for volumes?

The volume of the empty space can be represented as follows

volume of the empty space = volume of cube - volume of sphere

Therefore,

volume of sphere = 4 / 3 πr³

where

• r = radius

Volume of cube = L³

where

• L = side length

Therefore,

volume of cube = 9³

volume of sphere = 4 / 3 π(4.5)³

Hence,

volume of the empty space = 9³ -  4 / 3 π(4.5)³

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