What's the volume of this 3D shape?

[jais4475]

I urgently need to calculate the volume of this shape but don't know how! All the lengths I know are listed on the first image, is it possible to calculate the volume with just these 4 numbers? This is the roof of a netted animal enclosure so I do not know angles etc. The green line would be the height of the shape from the centre of the shape, sorry for the poor illustration! Can anyone please help??

 

[Farzin]

View attachment 17077View attachment 17078

I urgently need to calculate the volume of this shape but don't know how! All the lengths I know are listed on the first image, is it possible to calculate the volume with just these 4 numbers? This is the roof of a netted animal enclosure so I do not know angles etc. The green line would be the height of the shape from the centre of the shape, sorry for the poor illustration! Can anyone please help??

 

[Dr.Peterson]

I suppose this is a case where we can just show the answer, as you need the result rather than to learn geometry -- assuming I can trust that this is not really a class exercise in disguise.

Each end is a pyramid whose base is a rectangle 7.77 by 4.7 m, that is, (12.24-2.84)/2, and whose altitude is 1.98 meters. The volume is the area of the base (7.77*4.7), times the height (1.98), divided by 3: 24.1 m^3. There are two of these.

The middle is a triangular prism "on its side", so its "base" is a triangle with base 7.77 m and height 1.98 meters, with area 7.77*1.98/2 = 7.6923 m^2; the "height" of the prism is 2.84 m, so the volume is 7.6923*2.84 = 21.85 m^3.

So the total volume is 2*24.1 + 21.85 = 70.05 cubic meters.

I've described the work so you can check my arithmetic.

As a check, though, if it were just a pyramid, the volume would be 1/3 LWH = 188.3/3 = 62.8; if it were just a gabled roof (prism), it would be 1/2 LWH = 188.3/2 = 94.2; and this is between the two. It would not be hard to make a general formula for the volume of a hipped roof.

 

[jais4475]

I suppose this is a case where we can just show the answer, as you need the result rather than to learn geometry -- assuming I can trust that this is not really a class exercise in disguise.

Each end is a pyramid whose base is a rectangle 7.77 by 4.7 m, that is, (12.24-2.84)/2, and whose altitude is 1.98 meters. The volume is the area of the base (7.77*4.7), times the height (1.98), divided by 3: 24.1 m^3. There are two of these.

The middle is a triangular prism "on its side", so its "base" is a triangle with base 7.77 m and height 1.98 meters, with area 7.77*1.98/2 = 7.6923 m^2; the "height" of the prism is 2.84 m, so the volume is 7.6923*2.84 = 21.85 m^3.

So the total volume is 2*24.1 + 21.85 = 70.05 cubic meters.

I've described the work so you can check my arithmetic.

As a check, though, if it were just a pyramid, the volume would be 1/3 LWH = 188.3/3 = 62.8; if it were just a gabled roof (prism), it would be 1/2 LWH = 188.3/2 = 94.2; and this is between the two. It would not be hard to make a general formula for the volume of a hipped roof.

Thank you so much!! This is super helpful, don't worry I am in university doing a dissertation on enclosure usage for a biology course and need to calculate the enclosures total volume but am a bit rusty on my maths!
Thank you again!

 

[Dr.Peterson]

In this case, if you need to do something like it again, you can just search for something like "volume of hip roof" and find sites that tell you how, more or less the same way we did.

Or, use this formula: If the base is L units long by W units wide, and the ridge is R units long (parallel to L) and H units high, then the volume is

WH(2L + R)/6​

In your example, this is (7.77)(1.98)(2(12.24) + 2.84)/6 = 70.05 cubic meters.