Question

A vessel is in the form of an inverted cone of height 6cm and radius 4cm and it is filled with water up to the r cm.. When lead shots its off each is a sphere of a radius 0.2cm are dropped into the vessel. One tenth of the water flows out. Find the no of lead shots into the dropped of vessel

Answer 1

Height of cone h=6cm

Radius of cone r=4cm

Volume of cone=

$\frac{1}{3} \pi \: r ^{2} h$

$\frac{1}{3} \times \frac{22}{7} \times 4 \times 4 \times 6 = \frac{704}{7} {cm}^{3}$

Now, radius of spherical lead shot R=0.2cm

Volume of 1 lead shot=

$\frac{4}{3} \pi \: {r}^{3}$

$\frac{4}{3} \times \frac{22}{7} \times {0.2}^{3} = \frac{88}{2625} {cm}^{3}$

Let the no. of lead shots be= n

Given, one tenth of the water flows out when the lead shots are dropped in the conical vessel.

=> 1/10 volume of cone= n×volume of lead shots

$\frac{1}{10} \times \ \frac{704}{7} = n \times \frac{88}{2625}$

$n = \frac{2625 \times 704}{10 \times 7 \times 88 }$

$n = 300$

Therefore, no. of lead shots dropped in the vessel=300

Answer 2

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