How to calculate the volume of a cone and hemisphere
Vložit
- čas přidán 2. 08. 2024
- How to calculate the volume of a cone and hemisphere.
This is around a level A question at GCSE - although it should be relatively straightforward if you show a clear, logical approach. The cone is 10cm tall and 12cm at the base; it's attached to a hemisphere (half a ball) and you are asked to calculate the volume.
There are some additional questions on www.mathswrap.co.uk.
I hope the video helps and please do add a comment below - thanks.
Visit www.mathswrap.co.uk real maths, tips and techniques.
i was struggling with a similar problem in my maths textbook, thank you so much for explaining! I’m from South Africa so it’s nice to see maths uniting the world haha
you are so much better than my math teacher I don't understand most of the stuff that comes out of his mouth, you make it so much clearer
you are so good at explaining math! you just gained a subscriber. Thank You sir :)
+ArabGurl - Glad to help :-)
Someone who helps! Thanks!
Great thank you for the tutorial.
That was really helpful! Thanks so much for your help!
Brian Luong Glad to help :-)
Very well demonstrated, Thank you, Steve from Ireland.
+@foxtrot55 - Glad to help :-)
What do you do if the height is the length of the cone and hemisphere? How do you work the height of the cone itself?
I doubt you still need help but if it gives you the radius then that is also the height of the hemisphere since the radius is a line that goes from the centre to anywhere in the sphere
Thankyou highly Simon you Are a light in my life
Merci beacoup, this help me a lot, Merci
Thank you! It has helped me to do my homework and I understand it well now. Thank you again!
np
OMG! This helped so much! Thank you!
+tiana mik - Glad to help :-)
This was really helpful, thanks a lot
Antonio Akridas That's great and glad to help :-)
i have this question and the radius of the cone and hemisphere is 4cm and the overall height is 14cm how do I do this?
+XxX_TonyBlair_XxX - Hi - thanks for this and here's the video:
czcams.com/video/quNBJCOZtJ8/video.html
All best S :-)
Thank u so much .makes so much sense now
Hey Simon every time I try to work it out on the calculator is says syntax error please help
it was very helpful for me thanks for this video.
+dawit hagos - Glad to help and all best with your studies :-)
That' s great, thanks for letting me know :-)
Thank you was helpful
Very welcome and glad to help - all best S :-)
Thanks ..You made it look simple,..i hope I get similar question like this in my exams...;)
+Kavi - Glad to help and all best for your exams S :-)
Hi so I'm just wondering how your sphere total came to such a high number and if its possible to show me how you can do this question without a calculator . As when i do my volume of a sphere i multiplied the pi by 6x6x6 what did i do wrong ? Thank you for your time :).
+Naomi Anderson - Hi - you might be asked to calculate the volume, without a calculator, by leaving the answer as a multiple of pi.
If the radius is 6cm the volume would be:
4/3 x pi x rcubed
4/3 x pi x 6 x 6 x 6
288pi cmcubed
I hope this helps and all best S :-)
thank you ever so much!!!
+BanterComedy - Glad to help and all best S :-)
I like his videos 🥰
Big help😭 😍thanks a lot , by the way hi! 2020 👋😁
what to do if u dont have the radius but you have the volume
Maze
Put the volume and calculate the equation. Let's say the volume is 25cm cube.
25= 1/3 × pi × r square.
25÷(1/3 × pi )= r square
Then the reduce is the root of 25÷(1/3×pi)= r
Exercise more the rules of how to solv equation usually by cross multiplication or division then it will be more easy.
thanks so much!
+Victor Nguyen (Pronounced Win) - No prob and all best with your studies :-)
a hemisphere is pasted on a cone along their planer faces the radius of base of hemisphere is 25cm and that of cone is 20cm and the height of cone is 15cm. also complete base of cone lies inside planer base of hemisphere. find the total surface area of the structure formed
how would you calculate surface area
damn this guy good
Thanks homie
might help if you wrote it out 1/3 x tt or 3.142 x6x6x10 got confused for a second
but thanks for help
tt=π I assume?
Is there a formula like 1/3πr^2(h+2r)
Hi - sorry - I'm really not sure ... it doesn't look familiar. Best S :-)
nice
I have a question if the radius is 6ft will it be half of it? Would it be 3ft? For the radius?
Hi - the radius is half the diameter. So, if the diameter is 6ft, then the radius would be 3ft. Best S
@@3minutemaths thank you!
I got a maths question saying “ a come is attached to a hemisphere of radius 3cm . The total height is 12cm find the volume?” Can you help me please I really don’t understand . I have watched your videos I get it but my results aren’t correct
Hi - hopefully this will help: czcams.com/video/quNBJCOZtJ8/video.html. Best S
I have this question but the question is not giving any measurements other than the height! How do you sort out this problem?
Hi - are you able to type the question in the comments, or does it need a diagram? If only height is shown there should be a way of working out the radius - have they given you volume? ratio? a similar shape? Best S
@@3minutemaths Thank you for getting back to me. The question just shows the shape like the one you drew in this video, a cone on top of hemisphere, with one arrow on the side showing the height, there is like an X in the middle of the arrow that states the height. It asks to work out the volume.
@@nunalmagnuna Hi - really sorry, but there appears to be some information missing .... perhaps you'd need to talk to your teacher? Here's a playlist but they all have a way of working through: czcams.com/play/PLPglScc3TJ-PlelFaW9ZtqycWgRfGJ0iw.html. Best S
@@3minutemaths Thank you very much
what if the height was for both the hemisphere and the cone?
Hi - there should be a way of working out the radius ... happy to help if you can give me the question? All best S :-)
hello what if the height is not given and its say find H which is height
if I use 3.14 as pi, will it be the same?
Bia Santos no
yes it will be the same
Yes
What is the radius of the hemisphere and cone is x?
Hi - please could you post the question? There’s usually some way of working out the radius .... Best S
How would you calculate the surface area of this shape??????
+Katy x - Hi - great question, I'll post a video and let you know when done. The key formulas are:
surface area of a cone pi x r x L
surface area of a sphere is 4 x pi x rsquared
Hope that helps and all best S :-)
Simon Deacon Thanks very much. In the video can you please explain the solution WITH and WITHOUT the slant height (l) given. Thanks again. :)
+Katy x - Hi - here's the playlist as promised :-) czcams.com/play/PLPglScc3TJ-MASfN48EonxlHrcq1JW-n2.html
Is there a way for this to be done if the question only gave you the 10 cm length? i probably sound really stupid.
+Anonymous Cat - You're not stupid - it's a great question. You'll always need a height and a radius although they sometimes need to be worked out. One of the favourite exam questions is to give 'slant height' of the cone ... you then need to use pythagorus (usually) to work out the actual height. All best S :-)
+Simon Deacon
Ah Makes Sense, it was one of the questions in my maths gcse test that i did on Wednesday. i completely blanked out and left it. it was on a non calculator test and i think they wanted it in terms of pi. oh well i guess its over and it wont pop up on the calculator test which is tomorrow. Thanks.
+Anonymous Cat - That's great and all best for the calculator test :-)
I have a question, how to half 404.896 is 452.448????
how is*
Why do you use 3.142 and not 3.14 for PI?
Hi - For most calculations 3.142 or 3.14 is absolutely fine for pi, and the value is usually given on the exam paper. As a matter of interest, pi was recently calculated to 31.4 trillion decimal places!
Understood....thank you so much
Are the videos from 2006 really helping?
Josh Magennis Army - This one’s 2013 and it’s a fairly popular question. All best with your exams :-)
@@3minutemaths cheers I have the gcse tomorrow so I've just been watching everything on ur channel
@@3minutemaths by the way do you have any idea of what a pass would be in terms of percentage?
what if you only have the length of cone and the length of hemisphere and no radius? ?
+Teresa Mazzeo - Hi - this question might help :-) czcams.com/video/quNBJCOZtJ8/video.html
Can you say me answer
refersh....thank you..
I can't believe that kids like me who used to learn this are not kids anymore
Lol - yep, I'm now tutoring younger siblings :-)
How to find a half of hemisphere?
N7 RiZe Is that Movilla Petru? lol
Toprak Şen If he was white tho
i gave you a like because you said football not soccer :)
Lol :-)
thanxs
but the writing is too small
OK - glad the video helped and I'll try to write a little larger in the future :-)
You need a glasses then
Simon Deacon
thank u so much and please keep uploading some videos about several topics because i get the way u explain . so thanx
Your answer is wrong. If u do it on a calculator using the same equations then your total volume will equal 264piecm3
Hi - 264pi is more accurate than 829.38... although most of these questions will ask you to answer to 3 sig fig or 2 decimal places.
7:36 The volume of the hemisphere is wrong.
Hi - how so?
Oooh! When you wrote the volume of the sphere, the nine looked just like a four, so when you solved for the hemisphere, I thought you calculated incorrectly. My mistake😅
@@sweettea3879 Lol - no worries - my bad writing is always gets me into trouble :-)
life saver hahaha
+Yuki Uzumaki - Glad to help :-)
The first 4 digits of pi 3.141 not 3.142.
Hi - 3.142 is just rounded from 3.1415 ... although pi seems to go on forever. Here's pi to 10,000 decimal places www.math.utah.edu/~pa/math/pi.html. Best S
thanxs
but the writing is too smaĺl
wait a minute. this isnt 3 minutes
Who is here after the SAT haha
😀
We shall make it with your best explanations🦸🏂🌹🌹🌹🎀🧨
… and you working so hard! Thank you for all your effort and wishing you all the very best S :-)