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?

 

Answer 1

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