A vessel in the form of a hemisphereical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6cm and 4cm. Find the height of water in the cylinder.

Explanation

Since The water from hemispherical bowl is emptied into a cylinder.
So, the volume of bowl = volume of container
Now, According to question
Volume of hemispherical bowl = 2π/3 (radius^3)
Or, `v_(1)=(2π/3)R^3`
Or, `v₁ =(2/3) * 3.14 × 6^3 `
`v₁ = 452.16 cubic cm`.
And,Volume of cylindrical container=v₂= π radius^2 height
Or, `v₂ = πr^2h`
Or,` v₂= 3.14 xx 4^2 xx h`
` v₂= 50.24 h` cubic cm
Again
volume of bowl = volume of container
i.e v₁ = V₂
or,` 452.16 cubic
cm = 50.24 × h`
h= `452.16 /50.24`
i.e height = `h = 9` cm