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# Quick Maths question help?!? Watch

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

ThanksðŸ˜ƒ

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2. Bump

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3. 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:
The volume of the hemisphere is:
The total volume is:

The volume of the cylinder is:
Rearrange that to get:
4. 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.
5. Thanks so much for the reply!
I finally get it now and i realized where i went wrong.

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