Question

# The figure shows a cuboid. The area of the 3 faces A, B and C are $$48$$ $$\displaystyle { cm }^{ 2 }$$, $$40$$ $$\displaystyle { cm }^{ 2 }$$ and $$30$$ $$\displaystyle { cm }^{ 2 }$$ respectively. Find the volume of the cuboid.

Solution

## Let length, breadth and height of cuboid be l,b and h respectively. Then,Area of A = $$l\times b=48{ cm }^{ 2 }$$Area of B = $$b\times h=40{ cm }^{ 2 }$$Area of C = $$h\times l=30{ cm }^{ 2 }$$Now, $$\left( A\times B\times C \right) ={ l }^{ 2 }{ b }^{ 2 }{ h }^{ 2 }={ \left( lbh \right) }^{ 2 }=48\times 40\times 30$$$$\Rightarrow \quad lbh=\sqrt { 57600 } =240{ cm }^{ 3 }$$Volume of cuboid = $$lbh=240{ cm }^{ 3 }$$Mathematics

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