Hey! Sign in to get help with your study questionsNew here? Join for free to post

Quick Maths question help?!?

Announcements Posted on
Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
    • Thread Starter

    Name:  ImageUploadedByStudent Room1475698186.021267.jpg
Views: 14
Size:  135.7 KB

    Can someone explain this to me step by step please?
    I tried going on the mark scheme but i only understood half of it.


    Posted from TSR Mobile
    • Thread Starter


    Posted from TSR Mobile

    First you work out the Volume of the Ice Cream Cone thing. If the radius of the hemisphere is x, then the height is also x (both radii), so the height of the cone is 4x (5x-x).
    The volume of the cone is: \frac{\pi *r^2 *h}{3} = \frac{\pi * x^2 * 4x}{3} = \frac{4x^3 * \pi}{3}
    The volume of the hemisphere is: \frac{4 * \pi *r^3}{3} / 2 = \frac{2 * \pi * x^3} {3} = \frac{2x^3 * \pi}{3}
    The total volume is:  \frac{4x^3 * \pi}{3} + \frac{2x^3 * \pi}{3} = \frac{6x^3 * \pi}{3} = 2x^3 * \pi

    The volume of the cylinder is:  V = \pi * r^2 * h
    Rearrange that to get:  h = \frac{V}{\pi * r^2} = \frac{2x^3 * \pi}{\pi * (2x)^2} = \frac{2x^3 * \pi}{4x^2 *\pi} = \frac{x}{2}

    height of cone is 4x (as 4x= 5x -x) the x comes from the height of the sphere

    vol of cone = 1/3*pi*x^2*4x

    vol of 1/2 sphere=4/6*pi*x^3

    4/6 comes about as its half a sphere you must half it so 4/3 * 1/2

    vol of cylinder = h*pi*(2x)^2

    so 1/3*pi*x^2*4x + 4/6*pi*x^3= h*pi*(2x)^2

    rearange h = (1/3*pi*x^2*4x + 4/6*pi*x^3)/(pi*(2x)^2)

    simplify h = x/2

    I did this quickly so i might be wrong, hope it helps, please note though I don't know if my answer is right I know it may be as it contains only 1 power of x so I know its a length, which I know h is, for example if h contained x^2 that would imply it was an area and therefore be wrong.
    • Thread Starter

    Thanks so much for the reply!
    I finally get it now and i realized where i went wrong.

    Posted from TSR Mobile
Write a reply…


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: October 6, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

I want...
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read here first


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.