Algebra in Geometry

Quote:

Originally Posted by osmosis786

Please read the attached document need serious help thanks
(Speechless)

please ignore my writing unless it helps :P

thanks

1. h > 6x
otherwise the sphere wouldn't submerge completely.

2. The volume of the sphere $\left(V_{sphere}=\dfrac43 \cdot \pi \cdot (3x)^3 = 36 \pi x^3\right)$ is added to the water.

3. To calculate the increase of the height you have to transform the volume of the sphere into a volume of a cylinder with the same base area as the water:

$36 \pi x^3 = 16\pi x^2 \cdot a$

where a denotes the additional height:

$a = \dfrac{36 \pi x^3}{16\pi x^2} = \dfrac94 x$