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# Solution for A Cylindrical Tub of Radius 5 Cm and Length 9.8 Cm is Full of Water. a Solid in the Form of a Right Circular Cone Mounted on a Hemisphere is Immersed in the Tub. If the Radius of the Hemisphere is Immersed in the Tub. If the Radius of the Hemi-sphere is 3.5 Cm and Height of the Cone Outside the Hemisphere is 5 Cm, Find the Volume of the Water Left in the Tub (Take π = 22/7) - CBSE Class 10 - Mathematics

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ConceptVolume of a Combination of Solids

#### Question

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub (Take π = 22/7)

#### Solution

To find the volume of the water left in the tube, we have to subtract the volume of the hemisphere and cone from volume of the cylinder.

For right circular cylinder, we have

r = 5cm

h = 9.8 cm

The volume of the cylinder is

V1 = πr2h

=22/7xx5^2xx9.8

= 770cm

For hemisphere and cone, we have

r = 3.5 cm

h = 5 cm

Therefore the total volume of the cone and hemisphere is

V_2=1/3pir^2h+2/3pir^3

=1/3xx22/7xx3.5^2xx5+2/3xx22/7xx3.5^3

= 154 cm3

The volume of the water left in the tube is

V = V1 - V2

Hence, the volume of the water left in the tube is V = 616cm3

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Q: 7
Solution A Cylindrical Tub of Radius 5 Cm and Length 9.8 Cm is Full of Water. a Solid in the Form of a Right Circular Cone Mounted on a Hemisphere is Immersed in the Tub. If the Radius of the Hemisphere is Immersed in the Tub. If the Radius of the Hemi-sphere is 3.5 Cm and Height of the Cone Outside the Hemisphere is 5 Cm, Find the Volume of the Water Left in the Tub (Take π = 22/7) Concept: Volume of a Combination of Solids.
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