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# VOLUME

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A triangular prism has a volume of 75m^3 and a right triangular base of the area of 10m^2.

a) What is the length of the prism?

b) Sketch a possible prism.
Label its dimensions.

Oct 23, 2020

#1
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the length is 7.5m

dimensions of the base (and the top) are:  4m, 5m, √41m

Oct 23, 2020
#2
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You have not explained why Jugoslav.

You have not helped this person to learn anything.

Melody  Oct 23, 2020
#4
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The drawing is not to scale.  jugoslav  Oct 23, 2020
#3
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First here is a sketch of a right triangular prism: The triangular end has an area of 10 m2  as given

area * length = volume

10  * L = 75 m3

L = 7.5 m

Now find appropo dimensions which will give triangle area of 10 m2

area = 1/2 b * h

10 = 1/2 b h

20 = bh                     so b and h have to multiply to 20      easy ones would be   4 and 5

but you could pick ANYthing that multiplies to 20       10   and 2     or   6 and 3 1/3    etc

whatever you pick for b and h    the hypotenuse dimension will be found by Pythagorean theorem

4^2 + 5^2 = h^2         h = sqrt 41

So your sketch would look like this (if you use 4 5 sqrt 41) Oct 23, 2020
#5
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Thanks Guys :)

The most important thing to understand here is that

For ANY right prism, the volume is the area of the front face multiplied by how far back it goes.

Volume of prism = Area of front * depth

so in this case

75=10*?

Oct 23, 2020