Question

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

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Solution

Let the number of lead shots dropped =n

The total number of number of lead shots =1/4 volume of the conical vessel

Lead shots

Radius, r=0.5 cm

Volume, V=43 πr3

43.227.0.5×0.5×0.5=43×227×0.125

Cone

Radius, r=5 cm

Height, h=8 cm

Volume, V=13πr2h

=13.227×5×5×8=13×227×200

14th volume=14×13×227×200

Total volume of number of shots

=n×43×227×0.125

n×43×227×0.125=14×13×227×200

n=14×13×227×200×34×722×10.125

=2004×4×0.125=2002=100

∴ The number of lead shots =100

The total number of number of lead shots =1/4 volume of the conical vessel

Lead shots

Radius, r=0.5 cm

Volume, V=43 πr3

43.227.0.5×0.5×0.5=43×227×0.125

Cone

Radius, r=5 cm

Height, h=8 cm

Volume, V=13πr2h

=13.227×5×5×8=13×227×200

14th volume=14×13×227×200

Total volume of number of shots

=n×43×227×0.125

n×43×227×0.125=14×13×227×200

n=14×13×227×200×34×722×10.125

=2004×4×0.125=2002=100

∴ The number of lead shots =100

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