Question
How many spherical lead shots each of diameter 4.2cm can be obtained from a solid rectangular lead piece with dimensions 66cm × 42cm × 21cm.
✓
Answer
Given that, lots of spherical lead of shots made from a solid rectangular lead piece.
$\therefore$ Number of spherical lead shots
$=\frac{\text{volume of solid rectangular lead piece}}{\text{volume of a spherical lead shot}}\ ...(\text{i})$
Also, given that diameter of a spherical lead shot i.e. sphere = 4.2cm
$\therefore$ Radius of a spherical lead shot,
$\text{r}=\frac{4.2}{2}=2.1\text{cm}[\therefore\text{radius}=\frac{1}{2}\text{diameter}]$
So, volume of a spherical lead shot i.e.
$\text{sphere}=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(2.1)^3$
$=\frac{4}{3}\times\frac{22}{7}\times2.1\times2.1\times2.1$
$=\frac{4\times22\times21\times21\times21}{3\times7\times1000}$
Now, length of rectangular lead piece, l = 66cm
Breadth of rectangular lead piece, b = 42cm
Hieght of rectangular lead piece, h = 21cm
$\therefore$ Volume of a solid rectangular lead piece i.e.
cuboid = l × b × h = 66 × 42 × 21
From Eq. (i), Number of spherical lead, shots
$\frac{66\times42\times21}{4\times22\times21\times21\times21}\times3\times7\times1000$
$=\frac{3\times22\times21\times2\times21\times21\times1000}{4\times22\times21\times21\times21}$
$=3\times2\times250$
$=6\times250=1500$
Hence, the required number of spherical lead shots is 1500.
$\therefore$ Number of spherical lead shots
$=\frac{\text{volume of solid rectangular lead piece}}{\text{volume of a spherical lead shot}}\ ...(\text{i})$
Also, given that diameter of a spherical lead shot i.e. sphere = 4.2cm
$\therefore$ Radius of a spherical lead shot,
$\text{r}=\frac{4.2}{2}=2.1\text{cm}[\therefore\text{radius}=\frac{1}{2}\text{diameter}]$
So, volume of a spherical lead shot i.e.
$\text{sphere}=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(2.1)^3$
$=\frac{4}{3}\times\frac{22}{7}\times2.1\times2.1\times2.1$
$=\frac{4\times22\times21\times21\times21}{3\times7\times1000}$
Now, length of rectangular lead piece, l = 66cm
Breadth of rectangular lead piece, b = 42cm
Hieght of rectangular lead piece, h = 21cm
$\therefore$ Volume of a solid rectangular lead piece i.e.
cuboid = l × b × h = 66 × 42 × 21
From Eq. (i), Number of spherical lead, shots
$\frac{66\times42\times21}{4\times22\times21\times21\times21}\times3\times7\times1000$
$=\frac{3\times22\times21\times2\times21\times21\times1000}{4\times22\times21\times21\times21}$
$=3\times2\times250$
$=6\times250=1500$
Hence, the required number of spherical lead shots is 1500.
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