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# 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 1m2 (metre squared), the front and back were each 0.75m2 and the sides were each 0.48m2. “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 m3, 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

H = 0.75B

But BxH = 0.48

Therfore B = 0.48/H

So, H = 0.75 x 0.48/H

Multiplying by H gives:

H2 = 0.75x0.48

H2= 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 m3 = 600 litres