Question

A beaker is completely filled with water

​A ball in the shape of a sphere ​with radius 4 centimeters is placed in the beaker and is completely ​submerged, causing the volume of water equal to the ball’s volume to ​overflow.
​​All of the water that overflows is collected in a funnel in the ​shape of a cone.
​​When the funnel is held vertically, the surface of the ​water collected forms a circle of radius 4 centimeters.
​What is the ​height of the cone formed by the water in the funnel?
​​Round your ​answer to the nearest inch.

Answer 1

Answer:6.3 in.

Explanation:

Given

Radius of sphere
`r=4\ cm`

When ball is immersed in beaker, it causes the water to flowout of beaker which is collected in the conical vessel

Such that amount of water equivalent to sphere volume is collected in it.

volume of ball

`V_s=(4\pi )/(3)r^3`

`V_s=(4\pi )/(3)* 4^3`

`V_s=(256\pi )/(3)\ cm^3`

Now volume of water collected is in shape of cone then volume of cone

`V_c=(\pi )/(3)r^2h`

and
`V_s=V_c`

`(256\pi )/(3)=(\pi )/(3)(4)^2* h\ quad [\text{h=height of cone formed}]`

`h=4^2=16\ cm\approx 6.29\approx 6.3\ in.`