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Question

The surface area of 3 different surfaces of a cuboid is 150cm2, 75cm2 & 50cm2. Find volume of cuboid.

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Solution

Total surface area of a cuboid of length l , breadth b and height h is
TSA=2(lb+bh+lh)
Given:-
l×b=150cm2b×h=75cm2h×l=50cm2
We know that volume of cuboid is
V=l×b×h
Squaring both the sides
V2=l2×b2×h2V2=l×l×b×b×h×hV2=(l×b)(b×h)(l×h)V=(l×b)(b×h)(l×h)
From the given equations
V=150×75×50V=52×3×2×52×3×52×2V=56×32×22V=53×3×2V=125×6V=750cm3

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