Question

ownicu.
8. How many lead shots each 3 mm in diameter can be made from a
cuboid of dimensions 9 cm x 11 cm x 12 cm?
$\pi = 22 \div 7$
​

Answer 1

$\huge{\bold{\underline{Solution:}}}$

The volume of the cuboid will be same as that of the lead shots.

Cuboid.

Given:

• length of cuboid, l = 9 cm
• breadth of cuboid, b = 11 cm
• height of cuboid, h = 12 cm

We know,

$\quad \bold{Volume \: of \: Cuboid = l \times b \times h} \\ \Rightarrow 9 \times 11 \times 12 \\ \Rightarrow 1188 \: cm^3$

Lead Shot:

Given:

• radius of lead shot, r = $\frac{0.3}{2} \: cm$

We know,

$\bold{Volume \: of \: Sphere = \frac{4}{3} \pi r^3} \\ \Rightarrow \frac{4}{3} \times \frac{22}{7} \times \left( \frac{0.3}{2} \right)^3 \\ \Rightarrow \frac{\cancel{88}}{\cancel{21}} \times \frac{0.027}{\cancel{8}} \\ \Rightarrow \frac{11}{\cancel{3}} \times \cancel{0.009} \\ \Rightarrow 0.033 cm^3$

No. of balls:

$\quad \bold{\frac{Volume \: of \: cuboid}{Volume \: of \: Lead \: shot}} \\ \Rightarrow \frac{1188}{0.033} \\ \Rightarrow 36000$

Therefore, 3600 Lead shots will be made from the cuboid.