Question

how many spherical lead shots each 4.2 cm in diameter can be obtained from a solid rectangular lead piece with dimension 6cm ×42cm × 21cm

Answer 1

hello!!!

spherical lead shot
r =21/10

rectangular lead piece (cuboid)
l=66. b=42 h=21

now
no of lead shot = vol of cuboid ÷ vol of lead shots
answer is 1500

Answer 2

Let number of headshots be x.

Volume of lead in the rectangular solid =(66×42×21)cm3 

Radius of a lead shot = 4.2/2 cm = 2.1 cm

Volume of a spherical lead shot = 4π×(2.1)3cm3

Volume of x spherical lead shots =

= [(4/3) × (22/7) × (2.1)^3 × x )] cm^3

Volume of x spherical shots = Volume of lead in rectangular solid

(4/3 × 22/7 × (2.1)^3 × x ) = 66 × 42 × 21

⇒ x = 66 × 42 × 21 × 3 × 7/4 × 22 × (2.1)^3

⇒x = 1500

∴ Number of lead shots=1500

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