How many solid spheres of diameter 2.1 dcm each can be made by melting a solid rectangular parallelopiped copper piece of length 6.6 dcm , of breadth 4.2 dcm and of thickness 1.4 dcm ? How many cubic - dcm metal will possess in each sphere ?

Explanation

The length of copper piecec = 6.6 dcm
= 66 cm
The breadth of copper piece = 4.2 dcm
= 42 cm
Height of copper piece = 1.4 dcm
= 14 cm
So , the volume of coper piece = ` ( 66 xx 42 xx 14) ` cc
The diameter of each piece = `(66 xx 42 xx 14) ` cc
The diameter of each sphere = 2.1 dcm = 21 cm
` :.` the radius of each sphere ` = 21/2 ` cm
` :. ` the volume of each sphere = `21/2 ` cm
` :.` the volume od each sphere =` 4/3 xx 22/7 xx (21 xx 21 xx 21 )/(2 xx 2 xx 2 ) `
` = 11 xx 21 xx 21` cc
Let the number of sphere = ` 11 xx 21 xx 21 ` cc
` = (11 xx 21 xx 21 )/(1000) ` cubic - dcm = 4.851 cubic dcm
Hence , the required number of sphere is 8 and the volume of each sphere is 4.851 cubic - dcm