Question

Find the volume of a sphere whose surface area is 1256 sq.cm (Take π = 3.14)​

Answer 1

Curved surface area of a sphere =1256 cm

2

We know that, Curved surface area of a spehre =4πr

2

⟹1256=4×3.14×r

2

⟹r

2

=

4×3.14

1256

⟹r

2

=100

∴r=10 cm

Hence, the answer is 10 cm.

4186.66666666 volume of sphere

Answer 2

Answer:

$\large{\underline{\underline{\textsf{\textbf{Diagram : -}}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf 10\ cm}\end{picture}$

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Given : -}}}}}$

↠ Surface area of sphere = 1256 cm².

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{To Find : -}}}}}$

↠ Volume of sphere

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Using Formulas : -}}}}}$

$\small{\bigstar{\underline{\boxed{\sf{\pink{Surface \: area \: of \: sphere = 4\pi{r}^{2}}}}}}}$

$\small{\bigstar{\underline{\boxed{\sf{\pink{Volume \: of \: sphere = \dfrac{4}{3}\pi{r}^{3}}}}}}}$

$\small\bigstar$ Where :-

↠ π = 3.14

↠ r = radius

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Solution : -}}}}}$

$\small\bigstar$ Firstly, finding the radius of sphere by substituting the values in the formula :-

$\small{\dashrightarrow{\sf{Surface \: area \: of \: sphere = 4\pi{r}^{2}}}}$

$\small{\dashrightarrow{\sf{1256 = 4 \times 3.14\times {r}^{2}}}}$

$\small{\dashrightarrow{\sf{1256= 12.56\times {r}^{2}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{1256}{12.56}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{1256 \times 100}{12.56 \times 100}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{125600}{1256}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \cancel{\dfrac{125600}{1256}}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} =100}}}$

$\small{\dashrightarrow{\sf{Radius = \sqrt{100} }}}$

$\small{\dashrightarrow{\sf{Radius = \sqrt{ 10\times 10}}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{Radius=10 \: cm}}}}}$

$\normalsize{\bigstar{\underline{\boxed{\sf{\purple{Radius \: of \: sphere =10 \: cm}}}}}}$

Hence, the radius of sphere is 10 cm.

$\begin{gathered}\end{gathered}$

$\small\bigstar$ Now, finding the volume of sphere by substituting the values in the formula :-

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4}{3}\pi{r}^{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4}{3} \times 3.14 \times {(10)}^{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4 \times 3.14}{3} \times (10 \times 10 \times 10)}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12.56}{3} \times 1000}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12.56 \times 1000}{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12560}{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \cancel{\dfrac{12560}{3}}}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{Volume \: of \: sphere \approx 4186.66 \: {cm}^{3}}}}}}$

$\normalsize{\bigstar{\underline{\boxed{\sf {\purple{Volume \: of \: sphere \approx 4186.66 \: {cm}^{3}}}}}}}$

Hence, the volume of sphere is 4186.66 cm³.

$\begin{gathered}\end{gathered}$