Question

Prove that 1/v = 2/3 (1 / a + 1 / b + 1 / c) if the rectangular parallelopiped's Volume is v, length, width and height are a, b, c and the area of ​​the whole surface is s, respectively.


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Answer 1

Prove that 1/v = 2/3 (1 / a + 1 / b + 1 / c) if the rectangular parallelopiped's Volume is v, length, width and height are a, b, c and the area of the whole surface is s, respectively.

Answer 2

Explanation:

Solution

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Let length, breadth, and height of a cuboid are 6x, 5x, and 4x respectively.

Its total surface area;

=2(lb+bh+hl)

=2(6x×5x+5x×4x+4x×6x)

=2(30×x

2

+20×x

2

+24×x

2

)

=2×74×x

2

=148×x

2

But it is given that total surface area=33300sq.m

i.e. 148×x

2

=33300

⇒x

2

=

148

33300

⇒x

2

=225m

2

⇒x=

225

⇒x=15m

Dimensions of cuboid are;

6x=6×15=90m

5x=5×15=75m

and 4x=4×15=60m

Volume of cuboid=90×75×60 cubic metres=405000 cubic metres.