Exercise 20E

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of the top which is open is 5 cm. It is filled with water up to the rim. 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.

Height of cone = 8 cm Radius = 5 cm \[\begin{array}{*{35}{l}} Volume\text{ }=~1/3\text{ }\pi {{r}^{2~}}h  \\ =\text{ }1/3\text{ x }22/7\text{ x }5\text{ x }5\text{ x }8\text{ }c{{m}^{3}}  \\ =\text{...

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A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 m and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.

Radius of the hemisphere part (r) = 3.5 m = 7/2 m Volume of hemisphere \[\begin{array}{*{35}{l}} =\text{ }2/3\text{ }\pi {{r}^{3}}  \\ =\text{ }2/3\text{ x }22/7\text{ x }7/2x\text{ }7/2\text{ x...

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