Question

A vessel is in the form of inverted cone. Its height is 8cm and the radius of its top, which
is open, is 5cm. It is filled with water up to the brim. When lead shots, cach of which is
sphere of radius 0.5em are dropped into the vessel, one fourth of the water flows out.
Find the number of lead shots dropped in the vessel
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Answer 1

Answer:

given height of vessel (inverted cone)=8cm

radius of its top which is open =5cm

lead shots radius(sphere)=0.5cm

Step-by-step explanation:

now,volume of water flows=volume of leadshots

=1/3$\pi$r^2h=1/3×22/7×5×5×8=4400/21cm3

volume of water flows =volume of lead shots

=1/4 of the volume of water in cone

=1/4×4400/21=1100/21 cm3

let radius of the lead shot be R=0.5cm

now,

volume of lead shots(sphere)=4/3$\pi$R^3

=4/3×22/7×5/10×5/10×5/10=11/21 cm3

required number of lead shots

=volume of water flows out/volume of one lead shot

=1100/21/11/21=1100/21×21/11

=100

hence,there are 100 such lead shots

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