Question

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.

Answer 1

Given that, lots of spherical lead shots made out of a solid cube of lead.

∴ Number of spherical lead shots = `"Volume of a solid cube of lead"/"Volume of a spherical lead shot"`  ...(i)

Given that, a diameter of a spherical lead shot i.e., sphere = 4 cm

⇒ Radius of a spherical lead shot (r) = `4/2`

r = 2 cm   ...[∵ Diameter = 2 × Radius]

So, volume of a spherical lead shot i.e. sphere

= `4/3 pi"r"^3`

= `4/3 xx 22/7 xx (2)^3`

= `(4 xx 22 xx 8)/21 "cm"^3`

Now, since edge of a solid cube (a) = 44 cm

So, volume of a solid cube = (a)³

= (44)³

= 44 × 44 × 44 cm³

From equation (i),

Number of spherical lead shots

= `(44 xx 44 xx 44)/(4 xx 22 xx 8) xx 21` 

= 11 × 11 × 21

= 121 × 21

= 2541

Hence, the required number of spherical lead shots is 2541.