Volume of composite figures help please

[aklealea123]

Please help with this problem. If you can give the answer and explain how you got it also so I know in the future. I have done well with all of the others but this one has me stumped thanks in advance!

 

[mmm4444bot]

Hello aklealea. We're glad to help. Have you thought about the individual parts? The prism is a rectangular solid with triangular prisms at each end.

How would you calculate the volume of the rectangular section? (You may google volume formula box, if you don't have a textbook.)

The volume of each triangular part may be calculated by multiplying the area of the triangle by the width of the prism.

Please share whatever work you can. Feel free to ask specific questions about things you don't understand. There is a link to the forum guidelines below. Thank you!

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[The Highlander]

Please help with this problem. If you can give the answer and explain how you got it also so I know in the future. I have done well with all of the others but this one has me stumped thanks in advance!

Hi aklealea123,

You say you "have done well with all of the others"; does this mean that you have already worked on prism volumes?

We like to see what attempts (right or wrong) that you have made to solve your problem before offering specific advice, so we won't be giving you the answer or explaining how we got it unless and until we see some input from you.

I would normally direct you to somewhere else on the Internet where you could find out everything about prisms but to save (everyone's) time I will just tell you that you can calculate the volume of a prism thus:-

Volume = Area of the base x Height.

(eg: A cylinder is just a circular prism; have you been calculating the volumes of cylinders?)​

Hint: Start by imagining the two end pieces and the middle section as three separate solids that you can turn around in your hands and join back together to make the original complete solid; I'm sure you will understand that the volumes of each part will add up to the volume of the whole.

The mid-section of your solid is described as a rectangular prism (it's also a cuboid which I'm sure you already know how to calculate the volume of?) but if you were to stand it on its end it would then be a square prism; do you see that?

Also, since each end section is described as a triangular prism then you should consider the triangle as the base (whose area you need to find before calculating the volume).

Please attempt some calculations yourself and come back with your answers; we can then tell you if you're right or explain what you need to change in order to get to the correct answer. We're waiting patiently to see how you do.

[PS: The simplest way to show us your work may be to write it out (neatly) on paper and then post a picture of what you've done in here.]