Q. 164.3( 7 Votes )
A hemispherical bowl of internal radius
9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?
Answer :
Let n bottles are needed to empty the bowl,
Therefore,
Volume of bowl = Volume of 'n' bottles
For hemispherical bowl,
Radius, r = 9 cm
As we know,
Volume of a hemispherical bowl
Where r is the radius of hemisphere
Volume of bowl
For single cylindrical bottle,
Base radius, r = 1.5 cm
Height, h = 4 cm
As we know,
Volume of cylinder = πr2h
Where r is base radius,
h is height of cylinder.
Volume of one bottle = π(1.5)2(4) = 9π cm3
As,
Volume of bowl = volume of n bottles
486π = (9π)n
Hence, 54 bottles are needed to empty the bowl.
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PREVIOUSA building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?NEXTA solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height180 cm. Such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius to the cone.
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