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Quick Maths question help?!?

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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.

Thanks😃

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Reply 1

bluepearl7

Bump

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Reply 2

BobBobson

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}

(edited 7 years ago)

Reply 3

Tridant

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.