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Question
How many spherical bullets each of 5cm in diameter can be cast from a rectangular block of metal 11 dm x 1m x 5 dm?
Solution
Given that a metallic block which is rectangular of diameter 11dm x 1m x 5dm
Given that diameter of each bullet is 5cm
Volume of sphere `=4/3pir^2`
Dimensions of rectangular block = 11dm x 1m x 5dm
Since we know that 1dm =10-1 m
11x10-1x1x5x10-2m3 ………(1)
Diameter of each bullet = 5cm
Radius of bullet (r)=`d/2=5/2=2.5cm`
=25x10-2m
So volume=`4/3pi(25xx10^-2)^3`
Volume of rectangular block should be equal sum of volumes of n spherical
bulletsLet no of bullets be ‘n’
Equating (1) and (2)
55x10-2=n=`4/3pi(25xx10^-2)^3`
`(55xx10^-2)/(4/3xx22/7(25xx10^-2)^3)`=n
n=8400
∴ No of bullets found were 8400
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