Help Me Do Some Simple Sums
Having wandered round a number of pet shops over the last few days I am becoming less and less convinced that my fish tank really holds 39 litres[1. when filled empty to full, not accounting for substrate and other displacement items.]
Working out the volume of a box is no problem. If the box is (for example) 40 cm square and 45 cm high (these figures will become clear in a mo) then you just multiply length by width by height (LxWxH). So:
L x W: 40 x 40 = 1600 cm2
L x W x H: 40 x 40 x 45 = 72000 cm3
For ease of reference, turning that into litres which is what I want is simply dividing the result of L x W x H by 1000. Correct me (please!) if I’m wrong but I think this can be written as ((l*w*h)/1000). The result is 72 litres. Dandy.
Here’s my problem. This is the shape of my tank:
The grey shaded part is the tank. What I need to do is remove the yellow triangle volume from the square. Measurements are on the image above, height is the same as the tank at 45cm.
I just cannot for the life of me grasp how to work out the volume of the yellow shaded area. Anyone with more brains (and life-force) than me able to work out that volume? I know there’s something about 1/2 base x width x height or similar but I can’t find a good reference on the net (at 11.25 PM on Sunday night…)
On a related note I have added six new plants to the tank today – it was looking much bare. Picture is here (Photobucket link) taken with a Blackberry, I apologise for the quality!
George on November 17th, 2008
Hi Mate
Almost right – the area of a right angled triangle is base x height divided by 2. So, in your example that is 28 x 28 / 2 = 392 sq cm. Then multiplied by the height of the tank (45 cm) gives a volume of 17640 cc, which equates to 17.64 litres. So subtracting this from your calculation of 72 litres, gives a theoretical volume for your tank of 54.36 litres. Unless of course I have it wrong. You could take into account the thickness of the glass (cos I expect those are external measurements) but that won’t amount to many litres :-)