Three spherical balls of glass of radii 6,8 and r cm are melted and fo

1.	Three spherical balls of glass of radii 6,8 and r cm are melted and formed into a single solid sphere with radius 9 cm which will fit perfectly in a cylinder shaped box, what is the volume of the unauthorized/unoccupied part of the box?➣Need answer with step by step explanation.
Answer» $\large{\mathcal{\underline{\:\:\:\:Given\:\:\:\:}}}$ $\sf{Radius\:of\:the\:sphere\:,r\:=\:<klux>9</klux>\:cm}$ ${\mathcal{\underline{We\:know\:that,}}}$ $\begin{gathered}\:\underline{\boxed{\tt{Volume\:of\:sphere\:=\frac{4}{3}πr^3\:}}}\end{gathered}$ $\begin{gathered}\:\underline{\boxed{\tt{Volume\:of\:cylinder\:=πr^2h\:}}}\end{gathered}$ ⠀⠀⠀⠀⠀ $\sf{\underline{Now,By\:using\:formula}}$ $\sf{Volume\:of\:the\:given\:sphere\:=\frac{4}{3}×π×9^3}$ $\sf{So,volume\:of\:the\:given\:sphere\:=3053.63\:cm^3}$ As the sphere will FIT PERFECTLY in the cylinder shape box.So,the radius of cylinder will be 9 cm. $\sf{Height\:of\:the\:cylinder\:,h\:=2r}$ $\sf{\leadsto{Height\:of\:the\:cylinder\:,h\:=2×9\:cm}}$ $\sf{So,height\:of\:the\:cylinder\:,h\:=18\:cm}$ ⠀⠀⠀⠀⠀ $\sf{\underline{By\:using\:formula}}$ $\sf{Volume\:of\:the\:given\:cylinder\:=π×9^2×18\:cm^3}$ $\sf{So,volume\:of\:the\:given\:cylinder\:=4580.44\:cm^3}$ Volume of unauthorized/unoccupied part of the box = (volume of cylinder-volume of sphere) $\leadsto$ Volume of unauthorized/unoccupied part of the box = (4580.44-3053.63) cm³ $\leadsto$ Volume of unauthorized/unoccupied part of the box = 1526.81 cm³ $\begin{gathered}\:\:\:\underline{\boxed{\tt{Hence,the\:volume\:of\:unoccupied\:part\:of\:the\:box\:is\:\bf{1526.81\:cm³}}}}\end{gathered}$

Three spherical balls of glass of radii 6,8 and r cm are melted and formed into a single solid sphere with radius 9 cm which will fit perfectly in a cylinder shaped box, what is the volume of the unauthorized/unoccupied part of the box?➣Need answer with step by step explanation.

Answer»

$\large{\mathcal{\underline{\:\:\:\:Given\:\:\:\:}}}$

$\sf{Radius\:of\:the\:sphere\:,r\:=\:<klux>9</klux>\:cm}$

${\mathcal{\underline{We\:know\:that,}}}$

$\begin{gathered}\:\underline{\boxed{\tt{Volume\:of\:sphere\:=\frac{4}{3}πr^3\:}}}\end{gathered}$

$\begin{gathered}\:\underline{\boxed{\tt{Volume\:of\:cylinder\:=πr^2h\:}}}\end{gathered}$

⠀⠀⠀⠀⠀

$\sf{\underline{Now,By\:using\:formula}}$

$\sf{Volume\:of\:the\:given\:sphere\:=\frac{4}{3}×π×9^3}$

$\sf{So,volume\:of\:the\:given\:sphere\:=3053.63\:cm^3}$

As the sphere will FIT PERFECTLY in the cylinder shape box.So,the radius of cylinder will be 9 cm.

$\sf{Height\:of\:the\:cylinder\:,h\:=2r}$

$\sf{\leadsto{Height\:of\:the\:cylinder\:,h\:=2×9\:cm}}$

$\sf{So,height\:of\:the\:cylinder\:,h\:=18\:cm}$

⠀⠀⠀⠀⠀

$\sf{\underline{By\:using\:formula}}$

$\sf{Volume\:of\:the\:given\:cylinder\:=π×9^2×18\:cm^3}$

$\sf{So,volume\:of\:the\:given\:cylinder\:=4580.44\:cm^3}$

Volume of unauthorized/unoccupied part of the box = (volume of cylinder-volume of sphere)

$\leadsto$ Volume of unauthorized/unoccupied part of the box = (4580.44-3053.63) cm³

$\leadsto$ Volume of unauthorized/unoccupied part of the box = 1526.81 cm³

$\begin{gathered}\:\:\:\underline{\boxed{\tt{Hence,the\:volume\:of\:unoccupied\:part\:of\:the\:box\:is\:\bf{1526.81\:cm³}}}}\end{gathered}$

Three spherical balls of glass of radii 6,8 and r cm are melted and formed into a single solid sphere with radius 9 cm which will fit perfectly in a cylinder shaped box, what is the volume of the unauthorized/unoccupied part of the box?➣Need answer with step by step explanation.

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Three spherical balls of glass of radii 6,8 and r cm are melted and formed into a single solid sphere with radius 9 cm which will fit perfectly in a cylinder shaped box, what is the volume of the unauthorized/unoccupied part of the box?➣Need answer with step by step explanation.​

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Three spherical balls of glass of radii 6,8 and r cm are melted and formed into a single solid sphere with radius 9 cm which will fit perfectly in a cylinder shaped box, what is the volume of the unauthorized/unoccupied part of the box?➣Need answer with step by step explanation.