Question

A solid is in the form of a right circular cone mounted on a hemisphere
The radius of the hemisphere is 2.1 cmn and the height of the cone is
4 cm. The solid is placed in a cylindrical tub full of water in such a
way that the whole solid is submerged in water. If the radius of the
cylinder is 5 cm and its height is 9.8 cm, find the volume of the water
left in the tub
(CBSE 1996C, 2000)​

Answer 1

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Maths

Surface Areas and Volumes

Volume of Combined Solids

A solid is in the form of a...

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A solid is in the form of a right circular cone mounted on a hemisphere.The radius of the hemisphere is 3.5cm and the height of the cone is 4cm.The solid is placed in a cylindrical vessel ,full of water ,in such a way that the whole solid is submerged in water.If the radius of the cylindrical vessel is 5cm and its height is 10.5cm ,find the volume of water left in the cylindrical vessel ?

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ANSWER

Given, radius of the hemisphere,r=3.5cm

Now, since the solid is in the form of a right circular cone mounted on a hemisphere, 

then radius of base of the cone=radius of the hemisphere

⇒ radius of the base of the cone=r=3.5cm

Height of the cone,h=4cm

So,

volume of the solid=volume of the cone+ volume of the hemisphere

⇒ volume of the solid=31πr2h+32πr3

⇒ volume of the solid=31πr2(h+2r)

⇒ volume of the solid=31×722×(4+7)=141.16cm3

Now, radius of the base of the cylindrical vessel,r1=5cm

Height of the cylindrical vessel,h1=10.5cm

∴ Volume of the water in the cylindrical vessel==πr12h1=722×25×