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Quick Maths question help?!?

    • Thread Starter

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


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    • 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
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