CBSE Class 10CBSE
Account
It's free!

User


Login
Create free account


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution - From each end of a solid metal cylinder, metal was scooped out in hemispherical from of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. - CBSE Class 10 - Mathematics

ConceptConversion of Solid from One Shape to Another

Question

From each end of a solid metal cylinder, metal was scooped out in hemispherical from of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm.
The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire [Use  π=22/7]

 

Solution

Height of the cylinder (h) = 10 cm
Radius of the base of the cylinder = 4.2 cm

Volume of the cylinder =`pir^2h`

`=22/7xx(4.2)^2xx10`

`=554.4 cm^3`

Volume of hemisphere=`2/3pir^2`

`=2/3xx22/7xx(4.2)^2`

`=155.232 cm^3`

Volume of the remaining cylinder after scooping out the hemisphere from each end
Volume of original cylinder - 2 x Volume of hemisphere

=554.4 - 2 x 155.232

=243.936 cm3

The remaining cylinder is melted and converted to
a new cylindrical wire of 1.4 cm thickness.
So they have same volume and radius of new cylindrical wire is 0.7 cm.
Volume of the remaining cylinder = Volume of the new cylindrical wire

`243.936=pir^2h`

`243.936=22/7(0.7)^2h`

h=158.4 cm

∴The length of the new cylindrical wire of 1.4 cm thickness is 158.4 cm.

Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

Reference Material

Solution for question: From each end of a solid metal cylinder, metal was scooped out in hemispherical from of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. concept: null - Conversion of Solid from One Shape to Another. For the course CBSE
S