Question
How many spherical lead shots each of diameter 4.2cm can be obtained from a solid rectangular lead piece with dimensions 66cm, 42cm and 21cm.
✓
Answer
Given that, lots of spherical lead shots made from a solid rectangular lead piece.
$\therefore$ Number of spherical lead shots $=\frac{\text{Volume of solid rectangular lead piece}}{\text{Volume of a spherical lead shot}}\ \ \dots(\text{i})$
Also, given that diameter of a spherical lead shot i.e., sphere = 4.2cm
$\therefore$ Radius of a spherical lead shot, $\text{r}=\frac{42}{2}=2.1\text{cm}\ \ \Big[\because\text{radius}=\frac{1}{2}\text{diameter}\Big]$
So, volume of a spherical lead shot i.e., sphere
$=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(2.1)^3$
$=\frac{4}{3}\times\frac{22}{7}\times2.1\times2.1\times21$
$=\frac{4\times22\times21\times21\times21}{3\times7\times1000}$
Now, length of rectangular lead piece, l = 66cm
Breadth of rectangular lead piece, b = 42cm
Height of rectagular 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 special lead shots is 1500.
$\therefore$ Number of spherical lead shots $=\frac{\text{Volume of solid rectangular lead piece}}{\text{Volume of a spherical lead shot}}\ \ \dots(\text{i})$
Also, given that diameter of a spherical lead shot i.e., sphere = 4.2cm
$\therefore$ Radius of a spherical lead shot, $\text{r}=\frac{42}{2}=2.1\text{cm}\ \ \Big[\because\text{radius}=\frac{1}{2}\text{diameter}\Big]$
So, volume of a spherical lead shot i.e., sphere
$=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(2.1)^3$
$=\frac{4}{3}\times\frac{22}{7}\times2.1\times2.1\times21$
$=\frac{4\times22\times21\times21\times21}{3\times7\times1000}$
Now, length of rectangular lead piece, l = 66cm
Breadth of rectangular lead piece, b = 42cm
Height of rectagular 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 special lead shots is 1500.
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