Question

The length , breadth and height of a rectangular side are in the ratio $5:4:2$ . If its total surface area is $1216c{m}^2$ , find the volume of the solid.

Answer 1

Given that the ratio in length, breadth and height of a rectangular solid $=5:4:2$

Total surface area $1216{cm}^2$

Let's assume the length$=5x$, breath $=4x$, height $=2x$

Total surface area $=2[5x\times 4x+4x\times 2x+2x\times 5x]=[20x^2+8x^2+10x^2]=2\times 38x^2=76x^2$

So, $76x^2=1216\Rightarrow x^2=1216/76=16=4^2\Rightarrow x=4$

Hence the dimensions of the rectangular solid are

Length $=5\times 4=20cm$

Breadth $=4\times 4=16cm$

Height $=2\times 4=8cm$

and volume $=lbh=20\times 16\times 8=2560{cm}^3$