Learning how to work out volume of a prism can be very important for all sorts of applications – mainly in manufacturing and transportation.
A ‘prism’ is a shape with a constant cross section, such as a cardboard box. It basically means that if you cut the prism in half the shape will be the same in the middle:
Try the Quick Test volumes of 3D shapes
To work out the volume of the prism:

 sometimes this is given to you, particularly if the shape is fairly complicated
 if its not given you should be able to calculate – although it’s a good idea to draw a sketch of the cross section to make your working easier
 some exam questions might require a cross section to be calculated in stages
 ..and then multiply by the length
A fairly typical exam question would be either to calculate the volume directly.. or a more practical example, such as:
“A light bulb box measures 6cm x 6cm x 10cm.
The light bulbs are packed into cartons which measure 36cm x 36cm x 80cm.
Calculate the number of light bulb boxes that completely fill one carton.”
To answer the question you’ll need to work out –
 the volume of the carton
 the volume of the light box
 divide the carton volume by the light bulb box volume
So
View the videos on YouTube:
How to work out the volume of a cuboid / regular prism
How to work out the volume of a regular prism – exam question
How to work out the volume of a triangular prism
DJH Gaming says
this is so helpful for my level 7 homework
Just an Arianator says
Wait so the first thing you do is that called the cross section the thing
you did where you found the area of the triangle first?
Hsiu Hua Chen says
better consider gettin a better camera m8
AntRobotic says
Thanks so much maths test tommorow
Kevin Does Stuff says
This explains it alot
MrAllAround says
Brillient technique and this helped me a lot, i would say that the quality
of your mic is not very good but i cant complain as you are helping me pass
my GCSE’s. Just something to keepe in mind 😛 Thanks M8
TheRealEMC says
Thanks for the tutorial! could you possibly get an improved mic so I can
hear you better? Just saying.
Maria Evans says
Thank you
Citlali Cortes says
I have a my final tomorrow and this helped so much(: Thank you
Dalene Emberson says
Take an easier route.
3 x 4 x 7= 84. Now just go half of that number and say that half of 84 is
42
V= 42cm(3) < that three is supposed to come out as cubed sorry.
Daniel Mccann says
I have learning difficulties and if u we’re my teacher I world be the
smartest kid on earth I have learnt so mush from u u explained it easy as I
was able to understand which most teachers don’t do thank you now I’m ready
for my exam
Tima Ali says
I’ve got a test next week and im so ready for it thx to u!
Reece Tyree says
do you not half your answer?
faizia butt says
Sessle Gaming says
Thanks Simon 😛
Bio Works Entertainment says
Harjinder Saib says
Tomorrow is my final test
Mildred Mukombiwa says
Ok so I am in Africa,we use half base times height formula,plz help…
Leon Wilson says
Hi there, thanks for the video mate however im a bit confused as my
question has :
8×15 for the triangle, but then then 17 x 10 for the larger side?
Geordie B says
thanks lad this helped with my GCSE revision
Katy Chan says
Excellent explanation. Very clear and understandable. Just what I was
looking for. Thank you.
Fraser Holden says
thank you Simon I was really struggling but I think Iv’e got it no 🙂
Ashvika thurai says
this is actually helpful thanks so much 🙂
LPSSisters 00 says
Your voice kinda sounds like a robot. I think it’s because of the camera or
something, about to watch it, I see great comments so, I am hoping it’s
helpful.
theultimate118 says
Thanks
Freak MOB says
thank you soo much
Orian Jamieson says
thank you Simon i have a mock exam coming up and i have been stuck on
prisms for the whole of this week and u showed me how to do it so thank you
:/)D
Amien Hashim says
safe man
zamzam hussein says
thanks, besides this helped me very well
Eddie Franklin says
holy hell… helped me so much thanks heaps.
Jervon Rogers says
How to work out the volume of a triangular prism:
http://youtu.be/Hkb6W4qEVck
tom wright says
Great help much appreciated
Zoozoozoop12 Gaming says
Thanks a lot! Maths test next week!!!
Farzana Nasrin says
This helped me revise for my level 7 assessment coming up! Thanks!
hussainA176 says
Thanks ! This helped me a lot i got 88% marks
omar younes says
yess I got an A maths. Thanks so much, if it was not for this video then i
might not have got the A
Knuckles The Echidna says
You made it so simple! Thanks a lot.
Kalyani Choudhury says
thank you simon u r a teacher who can explain clearly u r so helpful thank
u so much
nate reeves says
thanks ur awsome
Bi Sian says
i mean different
Bi Sian says
in my class we use a diffrent formula
Bi Sian says
tnxs dude
Bi Sian says
helped a lot
Bi Sian says
yolo
SJ CFC7 says
thank you 🙂
Harvey Mullin says
Thanks
Atrix43993 says
awesome and the most simple video thxs helped me with my test and got
awesome marks THANKX
Zuu Baid says
THNQ sir … ^_^
Jehad Abdulwahab says
thanks appreciate it 🙂
Extrude Wreck says
thank you mate really helped.Got test tomorrow.
Paul Lee says
good!
Sefkan Sel says
Thanks I got stuck and you helped me a lot do more videos
Taylor Hardin says
Thank you so much! I don’t have a very good geometry teacher that explains
this stuff well and this helped me a lot!
Aamina Hasan says
thanks this helped
Tom C says
Thanks this helped a lot with my mock GCSE’s
Shahaan Soni says
thank you now i wont get a detention :)……………………..i
subscribed
BigBangTheoryBB says
Again, this helped a lot.
BigBangTheoryBB says
This helped so much! I’ve subscribed!!! 🙂
ashok gurung says
I got maths exam tomorrow and this has helped me to understand very easily!
Thanks a million 🙂
Callum Bickley says
you explained it so much more simpler 🙂
Amber R says
I was stuck for a maths test but I’m fine now thanks for the help!
SweetLittleMuffin says
Thank you so much! This video really helped a lot:)
Ochea Gilzene says
thanks do you think you could do a video of l shaped prisims
Nerf Leader says
This helped a lot,now i don’t have to worry about my homework!!
Abdool Khodabuccus says
i had (W)24cm (H)20cm and (L)53cm and i got 3052800cm(3)
Exdos Mania says
Hah i was stuck on this question and it had the exact same lenghts as the
ones you used in your video 🙂 thanks
Sattima Mignott says
what if you have all the sides of the triangle then what should you do
Ryan Hack says
Fantastic video, you definitely helped me with solving these types of
questions!
Chooi Li says
Thank you, this is really helpful!
Justin Lawrence says
Thanks this will really help out my angel on her SAX
James Davies says
Hey simon! Thanks a bunch really got me out of a tight spot with some
homework :”) – James
Mark Chambers says
Thank you for the great help!!
Minecraft is me says
Thanks it really helped
Darren Pritchard says
Omg I watched this the day before my maths test and it was in it!! I was so
grateful for those 3 extra marks that I came back to comment!! Thanks!
Grace Caldelas says
OMG i got an A+ on my test!! Thanks alot you helped so
much!!!!!!!!!!!!!!!!!!
Mckenzie Lamica says
This helped a lot! Finals tommorow, and this is a question, I’ll remember
just needed a quick refresher! Thanks!
Jbacltbe says
It was really helpful thank you and this question on 1380/3h june 2010
edexcel paper is worth 2 marks
Matthew M says
For some reason a Englishman explaining these things are more reassuring.
shabaz codmaster says
Thanks, this helped me a lot and hope that this kind of question appears in
2 weeks time on my maths exam.
Taha husain says
thank you MR Simon because of you i got 100% in exam
Sandith Elegoda says
Thanks alot u helped me alot thanks thanks
Shaun Wu says
Very useful and resourceful
Sameer Hussain says
You have really given me the way of working out volume as this was one of
the topics I was really stuck on! Thank you!
abdul majeed cheerangan kombath says
Thank you thankyou thankyou so much helped me a lot
aarushi mahajan says
Could you pls make a video for some of the complicated prisms as well. The
ones which pop up in exams frequently. Thanks.
Smiley Face Studios says
Good job on the video, you helped thousands of kids get the right answers
on that one math test tomorrow.(Including me.)
Concertvids says
This helped me so much! Thank you! 🙂
srsly Bailey says
Cheers boss
OnlineGamerPro26 says
Thanks
Tony Diep says
A+ on my test
MrTheGreenlander says
Thank you a lot. I must mention it was hard to hear you though 🙁
Seid Ali adowe says
I watch different videos,But I didn’t get it.
However this video was helpful to me. Pls keep up ur great job.
Dharmendra Patel says
when ever i need help on math you are always there with a video so thanks
!!
The force dude says
THANK U!!!!
damian barrios says
Very useful! Thank you so much
Salman Rahmani says
Thanks I got a 100 cause of u
A. Taylor says
thanks.
lucysimmo11 says
This video helped a lot I am revising for my yr 9 SATS thank you so much
clearer than bitesize and all the other online help
mrdarkevil1998 says
thanks
IBInum1 says
Thank you.. Helped me alot!
FlusherBox says
Thankyou
theflyingfalafel says
Saved my butt! Thanks!
ayesha ismail says
Good teaching method
Hannah Briggs says
Very helpful, thank you.
Mustace_man FTW says
THANK YOU!
Benita offical says
plz can you work out this question plzz if u dont mine (respected sir) !!!!!
find the value of 27 of 1/3 and
give that
8 ()square root of 18 divided by 2 square equal to a+b square of 2 where a
and
b are integers
and fine the value of a and the value of b
Thee Boss says
okllolrah
Mizzcutieboo says
thanks for explaining unlike my teacher, thanks !!!
Mali Ali says
It is brilliant video!
ibi num says
Thanks a lot it helpme out:D
tanay patel says
THANK UUUUU
hUnTeR95674 says
Thanks this really helped with my work
TheLaurenj says
Was actually really helpful:D thank you
Simon Deacon says
Hi – you’d need to know the depth. The area would be 1/2 (base x height) so:
1/2 (5 x 15) = 37.5 square inches.
Once you know the depth you should be able to work out the volume.
I hope this helps and all best
S
Glenn Angelo Diaz says
5. What is the volume of the triangular prism with the base edge of 5 inches and height of 15 inches?
Dylan Light says
great vid thx for the help! 🙂
Ayaz Vahora says
Thanks helped
Benoy Thomas says
Highly appreciated and Thank You very much.
Simon Deacon says
The comment took out my separation lines – I hope you can read this OK
Simon Deacon says
Hi – OK, you need a bit of algebra. Make the top 2x and the bottom 3x.
Area of a trapezium is 1/2 (a + b) x h
So,
600 = 1/2 (2x + 3x) x 15
600 = 1/2 (5x) x 15
40 = 1/2(5x)
40 = 2.5x
16 = x
If x = 16 then the top will be 32cm and the bottom is 48cm.
You can check by
Area = 1/2 (a+b) x h
and then putting the numbers in. You should get an area of 600cm2.
I hope this helps, it’s not easy to type out in a comment box!
All best
S
Benoy Thomas says
Kindly help to solve the below question.
The ratio of the parallel sides of a Trapezium is 2:3. The distance between them is 15cm. If the area of the trapezium is 600cm2, find the lengths of parallel sides.
Thanks & Best Regards.
Benoy Thomas says
Thanks.
FPSensati0n says
Great video mate ! Great help
Simon Deacon says
Glad it helped 🙂
Shamzz HD says
Thank you so much. Life saver.
Simon Deacon says
Hmm .. thanks. have been thinking about a label mike so will do now!
prabssbc says
Thanks! I do find the mic you are using…distracting..
wsam khaled says
thankkkkkkkkkk uuuuuuuuuuu
SuperDuperbenqled says
soz excuse ma spellin
SuperDuperbenqled says
thx matehelp ma alot
Shaun Whitaker says
thankx love i am so tankful p.s i love you
Eumesh Weerapura says
Thank you Sir.
ameera chaudhry says
thanku! u made every thing easier for me. it all makes sence now 🙂