Question

How many shots each having diameter $3\mathrm{cm}$ can be made from a cuboidal lead solid of dimensions $9\mathrm{cm}\times 11\mathrm{cm}\times 12\mathrm{cm}$?

Answer 1

Step 1: State the given data and formula used

Diameter of spherical shots $=3\mathrm{cm}$

Dimensions of cuboid,

Length $=9\mathrm{cm}$

Breadth $=11\mathrm{cm}$

Height $=12\mathrm{cm}$

We know that,

Volume of sphere $=\frac{4}{3}{\mathrm{\pi r}}^3$ ; $\left[r=\mathrm{radius}\mathrm{of}\mathrm{sphere}\right]$

Volume of cuboid $=\mathrm{l}\times \mathrm{b}\times \mathrm{h}$ ; $\left[l=\mathrm{length},b=\mathrm{breadth},h=\mathrm{height}\right]$

Step 2: Calculating the number of shots

Since the diameter of spherical shots $=3\mathrm{cm}$

so, the radius of spherical shots $=\frac{3}{2}\mathrm{cm}$ ; $\left[\mathrm{radius}=\frac{1}{2}\mathrm{diameter}\right]$

$=1.5\mathrm{cm}$

Since, the volume of a sphere $=\frac{4}{3}{\mathrm{\pi r}}^3$

$\Rightarrow$ the volume of one shot $=\frac{4}{3}\times \frac{22}{7}\times {(1.5)}^3$

$\Rightarrow$ the volume of one shot $=\frac{99}{7}{\mathrm{cm}}^3$

Again, since, the volume of cuboid $=\mathrm{l}\times \mathrm{b}\times \mathrm{h}$

$\Rightarrow$ the volume of cuboidal lead $=9\times 11\times 12$

$\Rightarrow$ the volume of cuboidal lead $=1188c{m}^3$

Now, number of shots $=\frac{\mathrm{Volume}\mathrm{of}\mathrm{cuboidal}\mathrm{lead}}{\mathrm{Volume}\mathrm{of}\mathrm{one}\mathrm{shot}}$

$\Rightarrow$ number of shots $=\frac{1188\times 7}{99}$

$\Rightarrow$ number of shots $=84$

Hence, $84$ shots can be made from the given cuboidal lead solid.