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Volume and Surface Areas of Solids — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsVolume and Surface Areas of Solids2 Marks
Question
A spherical shell of lead whose external and internal diameters are 24cm and 18cm, is melted and recast into a right circular cylinder 37cm high. Find the diameter of the base of the cylinder.
✓

Answer

External diameter of the shell = 24cm
External radius of the shell = 12cm
Internal diameter of the shell = 18cm
Internal radius of the shell = 9cm
Volume of the shell $=\frac{4}{3}\pi(12^3-9^3)=\frac{4}{3}\pi(1728-729)$
$=\frac{4}{3}\pi\times(999)=4\pi\times(333)\text{cm}^3$
Height of cylinder = 37cm
Let radius of cylinder be rem.
Volume of cylinder $=\pi\text{r}^2\text{h}=37\pi\text{h}^2\text{cm}^3$
Volume of the shell = Volume of cylinder
Or, $4\pi\times(333)=37\pi\text{r}^2$
$\Rightarrow\text{r}^2=\frac{4\times333}{37}=4\times9$
$\Rightarrow\text{r}\sqrt{4\times9}=\sqrt{36}=6\text{cm}$
So, diameter of the base of the cylinder = 2r = 12cm.

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