area to volume ,

Geometry Level 1

In the cuboid shown above, the area of the yellow region is 32, the red region is 8, and the green region is 16. Find the volume of this cuboid.

1 solution

Vilakshan Gupta
Feb 9, 2018

Let the length by $l$

Let the Breadth be $b$

Let the height be $h$

Area of yellow region $=lb=32$

Area of red region $=bh=8$

Area of green region $=lh=16$

Multiplying all the equation gives $l^2b^2h^2=32\times 8 \times 16=4096$

$\implies$ Volume = $lbh=\sqrt{4096}=\boxed{64}$

However, it is not difficult to see that $l=8$ , $b=4$ , $h=2$