# Boxing Clever

I asked a friend for measurements of the water tank he installed to collect rainwater to economise on his water charges. He reported back to me that the base was 1m^{2} (metre squared), the front and back were each 0.75m^{2} and the sides were each 0.48m^{2}. “That’s not what I meant”, I protested. “I wanted the volume, but never mind I can work it out!”

Can you figure out the volume of the tank?

Solution: 0.6 m^{3}, or 600 litres( length = 1.25m, breadth = 0.8 m, height = 0.6m)

Again we can tackle this with trial and error or with algebra

We will use L,B,H for length, breadth and height

LxB is area of the base

LxH = areas of the front and back

BxH = areas of the ends

So, we have thee equations and three unkowns so we should be able to get a unique answer for each parameter

LxB = 1

LxH = 0.75

BxH = 0.48

L = 1/B

L = 0.75/H

Therfore 1/B = 0.75/H

This leads to –

H = 0.75B

But BxH = 0.48

Therfore B = 0.48/H

So, H = 0.75 x 0.48/H

Multiplying by H gives:

H^{2} = 0.75x0.48

H^{2}= 0.36

H = 0.6m

And B = 0.48/H

B = 0.48/.6

B = 0.8m

And L = 1/B

Therefore L = 1/0.8

L = 1.25m

Volume = LxBxH

= 0.6x0.8x1.25 = .6 m^{3} = 600 litres