The Total solution for NCERT class 6-12
A vessel is in theform of an inverted cone. Its height is 8 cm and the radius of its top, whichis open, is 5 cm. It is filled with water up to the brim. When lead shots,
each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
For the cone,
Radius = 5 cm,
Height = 8 cm
Also,
Radius of sphere = 0.5 cm
The diagram will be like
It is known that,
Volume of cone = volume of water in the cone
= ⅓πr2h = (200/3)π cm3
Now,
Total volume of water overflown= (¼)×(200/3) π=(50/3)π
Volume of lead shot
= (4/3)πr3
= (1/6) π
The number of lead shots = Total Volume ofWater over flown/ Volume of Lead shot
= (50/3)π/(⅙)π
= (50/3)×6 = 100