The radius of the internal and external hallow spherical shell 3 cm and 5 cm respectively .After melting it is recasted into a solid cylinder of height 2*2/3 cm..What is the radius of cylinder
Answers
Answer:
Radius of cylinder = 7 cm
Step-by-step explanation:
Given ---> Internal radius of shell = 3 cm
Outer radius of cylinder = 5 cm
2
Height of cylinder formed = 2 ----- cm
3
= 8 / 3 cm
To find ---> Radius of cylinder
Solution --->
Volume of spherical shell =4/3 π (R³ - r³)
= 4 / 3 π { ( 5 )³ - ( 3 )³ }
= 4 / 3 π ( 125 - 27 )
= 4 / 3 π ( 98 ) cm³
Let radius of cylinder be r₁
Volume of cylinder = π r₁² h
= π r₁² ( 8 / 3 ) cm³
ATQ , Spherical shell is melted and recast in to cylinder so
Volume of spherical shell = volume of
cylinder
4/3 π × 98 = π r₁² ( 8/3 )
4/3 π is cancel out from both sides
=> 98 = 2 r₁²
=> r₁² = 98 / 2
=> r₁² = 49
=> r₁² = 7²
Taking square root both sides
=> r₁ = 7
Additional information--->
1) Volume of cone = 1/3 π r² h
2) Volume of sphere = 4/3 π r³
3) Volume of cube = edge³
4) Volume of cuboid = l × b × h
Answer:Radius of cylinder = 7 cm
Given ---> Internal radius of shell = 3 cm
Outer radius of cylinder = 5 cm
2 Height of cylinder formed = 2 ----- cm
3 = 8 / 3 cm
To find ---> Radius of cylinder
Solution --->
Volume of spherical shell =4/3 π (R³ - r³)
= 4 / 3 π { ( 5 )³ - ( 3 )³ }
= 4 / 3 π ( 125 - 27 )
= 4 / 3 π ( 98 ) cm³
Let radius of cylinder be r₁
Volume of cylinder = π r₁² h
= π r₁² ( 8 / 3 ) cm³
ATQ , Spherical shell is melted and recast in to cylinder so
Volume of spherical shell = volume of cylinder
4/3 π × 98 = π r₁² ( 8/3 )
4/3 π is cancel out from both sides
=> 98 = 2 r₁²
=> r₁² = 98 / 2
=> r₁² = 49
=> r₁² = 7²
Taking square root both sides
=> r₁ = 7