How many spherical lead shots each 4.2 cm in diameter can be obtained from a rectangular solid of lead with dimensions 66cm, 42cm, 21cm. `(u s epi=(22)/7)dot`

Explanation

Given that, lots of spherical shots made form a solid reactange lead piece.
`therefore` Number of spherical lead shots
`= ("Volume of solid rectangular lead piece")/("Volume of spherical lead shot")`
Also, given that diameter of a spherical lead short i.e., sphere = 4.2 cm
`therefore ` Radius of a spherical lead shot i.e., " "[`therefore` radius `- (1)/(2)` diameter]
So, volume of a sphereical lead shot i.e., sphere
`= (4)/(3) pir^(3)`
`" "=(4)/(3) pi r^(3)`
`" "= (4)/(3)xx (22)/(7) xx (2.1)^(3)`
`" " = (4)/(3)xx(22)/(7) xx 2.1 xx 2.1 xx 2.1`
`" "=(4 xx 22 xx 21 xx 21xx21)/(3xx7xx1000)`
Now, lenght of rectangular lead piece, l = 66 cm
Breadth of recatngular lead piece , b = 45 cm
Height of rectangular lead piece i.e., cuboid = `l xx b xx h = 66xx42xx21` From Eq. (i)
Number of spherical lead shots `=(66 xx 42 xx 21)/( 4 xx 22 xx 21xx21xx21) xx 3xx7 xx 1000`
` = (3 xx 22xx21xx2xx21xx21xx1000)/(4 xx 22 xx 21 xx 21)`
`= 3 xx 2 xx 250`
`= 6xx 250 = 1500.`
Hence , the required number of spherical lead shots is 1500.