Question
How many spherical bullets each of $5\ cm$ in diameter can be cast from a rectangular block of metal $11dm × 1m × 5dm?$
✓
Answer
We are given a metallic block of dimension $= 11\ dm × 1m × 5\ dm.$
We know that, $1 \mathrm{dm}=10^{-1} \mathrm{~m}$
So, the volume of the given metallic block is $=11 \times 10^{-1} \times 1 \times 5 \times 10^{-1}=55 \times 10^{-2} \mathrm{~m}^3$
We want to know how many spherical bullets can be formed from this volume of the metallic block. It is given that the diameter of each bullet should be $5\ cm.$
We know,
$\text{Volume of a sphere}=\frac{4}{3}\pi(\text{r})^3$
Here, $r = 25 × 10^{-3}m$
Let the no. of bullets formed be $n.$
We know that the sum of the volumes of the bullets formed should be equal to the volume of the metallic block.
$\Rightarrow55\times10^{-2}=\text{n}\times\frac{4}{3}\times\frac{22}{7}\times(25\times10^{-3})^3$
$\text{n}=\frac{55\times3\times7\times10^{-2}}{4\times22\times25\times25\times25\times10^{-9}}$
$=\frac{21\times10^7}{(2\times5)^3\times25}$
$=8400$
Hence the no. of bullets that can be formed is $8400$.
We know that, $1 \mathrm{dm}=10^{-1} \mathrm{~m}$
So, the volume of the given metallic block is $=11 \times 10^{-1} \times 1 \times 5 \times 10^{-1}=55 \times 10^{-2} \mathrm{~m}^3$
We want to know how many spherical bullets can be formed from this volume of the metallic block. It is given that the diameter of each bullet should be $5\ cm.$
We know,
$\text{Volume of a sphere}=\frac{4}{3}\pi(\text{r})^3$
Here, $r = 25 × 10^{-3}m$
Let the no. of bullets formed be $n.$
We know that the sum of the volumes of the bullets formed should be equal to the volume of the metallic block.
$\Rightarrow55\times10^{-2}=\text{n}\times\frac{4}{3}\times\frac{22}{7}\times(25\times10^{-3})^3$
$\text{n}=\frac{55\times3\times7\times10^{-2}}{4\times22\times25\times25\times25\times10^{-9}}$
$=\frac{21\times10^7}{(2\times5)^3\times25}$
$=8400$
Hence the no. of bullets that can be formed is $8400$.
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