Question

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

Answer 1

Given that, lots of spherical lead shots made from a solid rectangular lead piece.

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

Also, given that diameter of a spherical lead shot i.e., sphere = 4.2 cm

∴ Radius of a spherical lead shot, r = `4.2/2` = 2.1 cm   ...`[∵ "radius" = 1/2 "diameter"]`

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

= `4/3 π"r"^3`

= `4/3 xx 22/7 xx (2.1)^3`

= `4/3 xx 22/7 xx 2.1 xx 2.1 xx 2.1`

= `(4 xx 22 xx 21 xx 21 xx 21)/(3 xx 7 xx 1000)`

Now, length of rectangular lead piece, I = 66 cm

Breadth of rectangular lead piece, b = 42 cm

Height of rectangular lead piece, h = 21 cm

∴ Volume of a solid rectangular lead piece i.e., cuboid

= I × b × h

= 66 × 42 × 21

From equation (i),

Number of spherical lead shots 

= `(66 xx 42 xx 21)/(4 xx 22 xx 21 xx 21 xx 21) xx 3 xx 7 xx 1000`

= `(3 xx 22 xx 21 xx 2 xx 21 xx 21 xx 1000)/(4 xx 22 xx 21 xx 21 xx 21)`

= 3 × 2 × 250

= 6 × 250

= 1500

Hence, the required number of spherical lead shots is 1500.