Answer:
The maximum volume the cube could have is 729 cubic inches
Step-by-step explanation:
The total surface area of the cube equals the total area of material used.
Let A = total surface area of cube = 6L² where L = length of side of cube
Since A = total area of material used, A = 486 in²
So 486 in² = 6L²
L = √(486 in²/6)
= √81 in²
= 9 in
The volume of the cube V = L³ where L = length of side of cube
So, V = (9 in)³
= 729 in³
So the maximum volume the cube could have is 729 cubic inches.
The maximum volume that the box could have will be 729inches³.
Based on the information given, the first thing to do is to find the length of the shape. This will be:
Length = ✓(486/6)
Length = ✓81
Length = 9
Therefore, the volume of the cube will be:
= 9³
= 9 × 9 × 9
= 729 in³.
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