A perfume bottle is available in a hemispherical bottom with a conical cap, packed in a cylindrical transparent sheet, such that it just encloses the bottle. If the height of the pack is 14cm and diameter of its base is 14cm, find capacity of perfume; also find how much space is left between the bottle and the pack.
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height of cylinder = 14
diameter of cylinder = 14
radius of cylinder = 7
then radius of hemisphere= 7
height of hemisphere= 7
radius of cone =7
height of cone = total height -hemisphere height
= 14 - 7
= 7
capacity of perfume = 2÷3×π×rcube +1÷3×π×rsq×h
= 2÷3×π×343+1÷3×π×49
= 2÷3×π×343+1÷3×π×343
= 684÷3×π+343÷3×π
= 228.66π+114.33π
= 342.99π
gap between bottle and pack = volume of cylinder - volume of perfume bottle
= π×rsq×h-(2÷3×π×rcube+1÷3×π×rsq×h)
=343π-342.99π
=0.01π
diameter of cylinder = 14
radius of cylinder = 7
then radius of hemisphere= 7
height of hemisphere= 7
radius of cone =7
height of cone = total height -hemisphere height
= 14 - 7
= 7
capacity of perfume = 2÷3×π×rcube +1÷3×π×rsq×h
= 2÷3×π×343+1÷3×π×49
= 2÷3×π×343+1÷3×π×343
= 684÷3×π+343÷3×π
= 228.66π+114.33π
= 342.99π
gap between bottle and pack = volume of cylinder - volume of perfume bottle
= π×rsq×h-(2÷3×π×rcube+1÷3×π×rsq×h)
=343π-342.99π
=0.01π
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