Question

A metallic sphere of radius 4. 2 Cm is melted and recast into the -shape of a cylinder of radues 6 Cm Find the height of the cylinder

Answer 1

$\huge\bf\underline{Answer}$

Given:-

• A metallic sphere of radius 4.2 cm is melted

• the shape of a cylinder of radius 6 Cm

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Find:-

• the height of the cylinder

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Solution:-

$\small\tt\underline{Now\:find\:the\:volume\:of\:sphere:-}$

$\small\tt{•Let\:the\:radius=r}$

$\small\tt{•sphere = 4.2 cm}$

$\rightarrow$$\tt{Volume\:of\:sphere}$= ${\frac{4}{3}}$$\pi$$\small\tt{r^3}$

$\therefore$$\tt{Volume\:of\:sphere}$ =

${\frac{4}{3}}$$\pi$×$\small\tt{(4.2)^3}$

$\Rightarrow$Volume of cylinder with radius,

$\small\tt{• r = 6cm}$

$\small\tt{• height 'h' cm}$

$\therefore$$\small{\tt{Volume\:of\:cylinder =}}$ $\pi$$\small\tt{r^2}$$\small\tt{h}$

$\rightarrow$$\pi$×$\small\tt{6^2}$×$\small\tt{h}$= $\small\tt{36}$$\pi$$\small\tt{h}$

$\small\boxed{\tt{Volume\:of\: sphere = volume\:of\:cylinder}}$

$\rightarrow$${\frac{4}{3}}$$\pi$×$\small\tt{(4.2)^3}$ = $\small\tt{36}$$\pi$$\small\tt{h}$

$\small\tt\underline{Find\:height"h"\:of\:cylinder:-}$

$\tt{h}$=${\frac{4π×(4.2)^3}{3×36π}}$

$\tt{h}$=${\frac{4.2×4.2×4.2}{3×9}}$

$\tt{h}$= $\small\tt{1.4×1.4×1.4}$

$\tt{h}$= $\small\tt{2.744cm}$

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$\small\boxed{\tt{height\:of \:cylinder =2.744cm}}$