Question

A beaker is completely filled with water

Answer 1

Answer:6.3 in.

Step-by-step 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

$V_s=\frac{4\pi }{3}r^3$

$V_s=\frac{4\pi }{3}\times 4^3$

$V_s=\frac{256\pi }{3}\ cm^3$

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

$V_c=\frac{\pi }{3}r^2h$

and $V_s=V_c$

$\frac{256\pi }{3}=\frac{\pi }{3}(4)^2\times h\ quad [\text{h=height of cone formed}]$

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