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]

 

Answer 1

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

Volume of the cylinder =${\displaystyle \pi r^{2}h}$

${\displaystyle =\frac{22}{7}\times {\left(4.2\right)}^2\times 10}$

${\displaystyle =554.4c{m}^3}$

Volume of hemisphere=${\displaystyle \frac{2}{3}\pi r^2}$

${\displaystyle =\frac{2}{3}\times \frac{22}{7}\times {\left(4.2\right)}^2}$

${\displaystyle =155.232c{m}^3}$

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

${\displaystyle 243.936=\pi r^{2}h}$

${\displaystyle 243.936=\frac{22}{7}{\left(0.7\right)}^{2}h}$

h=158.4 cm

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