#### 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^{-1}x1x5x10^{-2}m^{3} ………(1)

Diameter of each bullet = 5cm

Radius of bullet (r)=`d/2=5/2=2.5cm`

=25x10^{-2}m

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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Solution 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? Concept: Volume of a Combination of Solids.