Originally Posted by

**jgv115** Ok let's do this:

The cone has a height of 4.4cm, the radius is 3.5 (same as hemisphere)

Let's do the cone first:

So grab the volume formula

$\displaystyle \frac {1}{3} * \pi * r^2*h $

$\displaystyle \frac {1}{3} * \pi * 3.5^2 * 4.4 $

You do it from there.

Now do the hemisphere

Sphere Formula:

$\displaystyle \frac {4}{3} * \pi * r^3 $

you need to divide by 2 because it is half of sphere

$\displaystyle \frac {\frac {4}{3} * \pi * r^3}{2} $

substitute radius in:

$\displaystyle \frac {\frac {4}{3} * \pi * 3.5^3}{2} $

You do it from there.

Then add together and done.

Second question:

Square based pyramid: The base has sides of 230m and the height is 147m.

I'm assuming the "material" is the volume... if I have misunderstood something then please say so...

Grab the formula:

$\displaystyle \frac {1}{3} *l*w*h$

$\displaystyle \frac {1}{3} * 230 * 230 * 147 $

$\displaystyle =2592100$

So we need 2592100 "material" to build a square based pyramid with base sides of 200m

Get the formula out again:

$\displaystyle V= \frac {1}{3} *l*w*h$

Substitute:

$\displaystyle 2592100 = \frac {1}{3} * 200 * 200 * h $

$\displaystyle 64.8025 = \frac {1}{3} * h $ <--- divide 200 two times.

$\displaystyle 194.408 = h $ <---- divide by 1/3 which is multiply by 3.

There's your height. The pyramid should use the same material.

Check:

$\displaystyle \frac {1}{3} * 200 * 200 * 194.408 $

$\displaystyle = 2592099.999999999 $ <---- basically the same..

ok that's it.