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Question
A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm3, will be required to fill the vessel completely?
Solution
Diameter of hemisphere = 7 cm
Diameter of the base of the cone = 7 cm
Therefore, radius (r) = 3.5 cm
Height (h) = 8 cm
Volume of the solid = `1/3pir^2h + 2/3pir^3`
= `1/3pir^2(h + 2r)`
= `1/3 xx 22/7 xx 3.5 xx 3.5(8 + 2 xx 3.5)`
= `77/6(8 + 7)`
= `385/2`
= 192.5 cm3
Now, radius of cylindrical vessel (R) = 7 cm
Height (H) = 10 cm
∴ Volume = πR2h
= `22/7 xx 7 xx 7 xx 10`
= 1540 cm3
Volume of water required to fill
= 1540 – 192.5
= 1347.5 cm3
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