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Surface Areas And Volumes — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsSurface Areas And Volumes3 Marks
Question
How many spherical bullets each of $5\ cm$ in diameter can be cast from a rectangular block of metal $11dm \times 1m \times 5dm$?
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Answer

We are given a metallic block of dimension $= 11dm \times 1m \times 5dm.$
We know that, $1dm = 10^{-1}m$
So, the volume of the given metallic block is $= 11 \times 10^{-1}\times 1 \times 5 \times 10^{-1} = 55 \times 10^{-2}m^3$
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, $r = 25 \times 10^{-3}​​​​​​​m$
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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