A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

Solution

Let r cm be the radius of the hemisphere, then r = 1 cm.
Let R be the radius of the cone and h cm be the height. Then

R = 1 cm and h = 1 cm
[It is given that R = h)
Now, Volume of solid
= Volume of hemisphere + volume of cone
$equals space 2 over 3 straight pi space straight r cubed plus 1 third space πR squared straight h equals space 2 over 3 straight pi space straight r cubed plus 1 third space straight pi space straight r squared straight h space space space space space left square bracket because space straight r space equals space straight R right square bracket equals space space 2 over 3 straight pi space left parenthesis 1 right parenthesis cubed plus 1 third straight pi left parenthesis 1 right parenthesis squared left parenthesis 1 right parenthesis equals space space 2 over 3 straight pi plus 1 third straight pi space equals space fraction numerator 3 straight pi over denominator 3 end fraction equals straight pi space cm cubed$

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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. 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.

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A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

Some More Questions From Statistics Chapter

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