Hey ! Buddy
There's a mistake in your question it's not T.S.A of cuboid it is T.S.A of cube . Because it's not possible to find the length , breadth and height of cuboid without giving only it's Total Surface Area .
Question : -
If TSA of cube box is 486 cm square , find its volume .
Given : -
- Total Surface Area ( T.S.A ) of cube is equal to 486 cm square .
To Find : -
Concept : -
For solving such types of questions we must have knowledge of faces of shapes and formula for surface areas and volumes of three dimensional shapes .
Formula Used : -
Solving Question : -
We know that cube have 6 faces . So area of each faces is equal to :
Now , dividing 486 by 6 :
Therefore , each square faces of cuboid have area of 81 cm square .
Now , We know that area of square :
Therefore , side/edge of cube is of 9 cm ..
Now , finding volume of cube :
We know that volume of cube is equal to ,
Therefore , volume of cube is 729 cm³ .
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