Answer:
[tex]\large{\underline{\underline{\textsf{\textbf{Diagram : -}}}}}[/tex]
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[tex]\begin{gathered}\end{gathered}[/tex]
[tex]\large{\underline{\underline{\textsf{\textbf{Given : -}}}}}[/tex]
↠ Surface area of sphere = 1256 cm².
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[tex]\large{\underline{\underline{\textsf{\textbf{To Find : -}}}}}[/tex]
↠ Volume of sphere
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[tex]\large{\underline{\underline{\textsf{\textbf{Using Formulas : -}}}}}[/tex]
[tex]\small{\bigstar{\underline{\boxed{\sf{\pink{Surface \: area \: of \: sphere = 4\pi{r}^{2}}}}}}}[/tex]
[tex]\small{\bigstar{\underline{\boxed{\sf{\pink{Volume \: of \: sphere = \dfrac{4}{3}\pi{r}^{3}}}}}}}[/tex]
[tex]\small\bigstar[/tex] Where :-
↠ π = 3.14
↠ r = radius
[tex]\begin{gathered}\end{gathered}[/tex]
[tex]\large{\underline{\underline{\textsf{\textbf{Solution : -}}}}}[/tex]
[tex]\small\bigstar[/tex] Firstly, finding the radius of sphere by substituting the values in the formula :-
[tex]\small{\dashrightarrow{\sf{Surface \: area \: of \: sphere = 4\pi{r}^{2}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{1256 = 4 \times 3.14\times {r}^{2}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{1256= 12.56\times {r}^{2}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{1256}{12.56}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{1256 \times 100}{12.56 \times 100}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{125600}{1256}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{{(Radius)}^{2} = \cancel{\dfrac{125600}{1256}}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{{(Radius)}^{2} =100}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Radius = \sqrt{100} }}}[/tex]
[tex]\small{\dashrightarrow{\sf{Radius = \sqrt{ 10\times 10}}}}[/tex]
[tex]\small{\dashrightarrow{\underline{\underline{\sf{Radius=10 \: cm}}}}}[/tex]
[tex]\normalsize{\bigstar{\underline{\boxed{\sf{\purple{Radius \: of \: sphere =10 \: cm}}}}}}[/tex]
Hence, the radius of sphere is 10 cm.
[tex]\begin{gathered}\end{gathered}[/tex]
[tex]\small\bigstar[/tex] Now, finding the volume of sphere by substituting the values in the formula :-
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4}{3} \times 3.14 \times {(10)}^{3}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4 \times 3.14}{3} \times (10 \times 10 \times 10)}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12.56}{3} \times 1000}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12.56 \times 1000}{3}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12560}{3}}}}[/tex]
[tex]\small{\dashrightarrow{\sf{Volume \: of \: sphere = \cancel{\dfrac{12560}{3}}}}}[/tex]
[tex]\small{\dashrightarrow{\underline{\underline{\sf{Volume \: of \: sphere \approx 4186.66 \: {cm}^{3}}}}}}[/tex]
[tex]\normalsize{\bigstar{\underline{\boxed{\sf {\purple{Volume \: of \: sphere \approx 4186.66 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of sphere is 4186.66 cm³.
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