Question

Que - the area of a circle is 55.44m2
find its radius​

Answer 1

$\large{\sf{\pmb{\underline{\purple{Given:-}}}}}$

● The area of a circle is 55.44 m²

$\large{\sf{\pmb{\underline{\purple{To \: Find :-}}}}}$

● Radius of Circle

$\large{\sf{\pmb{\underline{\purple{Formula \: Used:-}}}}}$

$\bigstar\underline{\boxed{\sf{\pink{Area \: of \: Circle ={\pi}{r}^{2}}}}}$

$\large{\sf{\pmb{\underline{\purple{Solution:-}}}}}$

${\underline{\frak{\pmb{\bigstar \: Here}}}}$

● Area of Circle = 55.44 m²

● Radius of Circle

${\underline{\frak{\pmb{\bigstar \: According \: To \: The \: Question}}}}$

${ : \implies{\sf{Area \: of \: Circle ={\pi}{r}^{2}}}}$

● Substituting the values

${ : \implies{\sf{55.44 \: {m}^{2} ={\pi}{r}^{2}}}}$

${ : \implies{\sf{55.44 \: {m}^{2} ={\dfrac{22}{7} } \times {r}^{2}}}}$

${ : \implies{\sf{\dfrac{55.44 \times 7}{22} = {r}^{2}}}}$

${ : \implies{\sf{\dfrac{\cancel{55.44} \times 7}{\cancel{22}} = {r}^{2}}}}$

${ : \implies{\sf{2.52 \times 7}= {r}^{2}}}$

${ : \implies{\sf{17.64 = {r}^{2}}}}$

${ : \implies{\sf{ \sqrt{17.64} = {r}}}}$

${ : \implies{\sf{r = 4.2 \: m}}}$

${\bigstar{\underline{\boxed{\sf{\pink{r = 4.2 \: m}}}}}}$

● Henceforth,The Radius of Circle is 4.2 m.

$\large{\sf{\pmb{\underline{\purple{Verification:-}}}}}$

${ : \implies{\sf{Area \: of \: Circle ={\pi}{r}^{2}}}}$

● Substituting the values

${ : \implies{\sf{55.44 \: {m}^{2} ={\pi}{r}^{2}}}}$

${ : \implies{\sf{55.44 \: {m}^{2} ={\dfrac{22}{7} } \times {(4.2)}^{2}}}}$

${ : \implies{\sf{55.44 \: {m}^{2} ={\dfrac{22}{7} } \times {(4.2 \times4.2) {m}^{2} }}}}$

${ : \implies{\sf{55.44 \: {m}^{2} ={\dfrac{22}{7} } \times {17.64 \: {m}^{2} }}}}$

${ : \implies{\sf{55.44 \: {m}^{2} ={\dfrac{22}{\cancel{7}}}\times{\cancel{17.64}\: {m}^{2} }}}}$

${ : \implies{\sf{55.44 \: {m}^{2} ={22}\times 2.52 \: {m}^{2} }}}$

${ : \implies{\sf{55.44 \: {m}^{2} =55.44 \: {m}^{2}}}}$

${\bigstar{\underline{\boxed{\sf{\pink{LHS=RHS }}}}}}$

● Hence Verified ✔

$\large{\sf{\pmb{\underline{\purple{Know \: More:-}}}}}$

$\begin{gathered}\small\begin{gathered}\bigstar \: \bf\underline{More \: Useful \: Formulae } \: \bigstar  \\ \begin{gathered}{\boxed{\begin{array} {cccc}{\sf{{\leadsto TSA \: of \: cube \: = \: 6(side)^{2}}}} \\  \\{\sf{{\leadsto LSA \: of \: cube \:= \: 4(side)^{2}}}}  \\  \\{\sf{{\leadsto Volume \: of \: cube \: = \: (side)^{3}}}} \\  \\ {\sf{{\leadsto Diagonal \: of \: cube \: = \: \sqrt(l^{2} + b^{2} + h^{2}}}} \\  \\ {\sf{{\leadsto Perimeter \: of \: cube \: = \: 4(l+b+h)}}} \\   \\ {\sf{{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}} \\  \\ {\sf{{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}} \\  \\{\sf{{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}} \\  \\ {\sf{{\leadsto Diameter \: of \: circle \: = \: 2r}}} \\  \\ {\sf{{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}} \\  \\ {\sf{{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}} \\  \\ {\sf{{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}} \\  \\ {\sf{{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}} \\  \\{\sf{{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}\end{array}}}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Step-by-step explanation:

$\begin{gathered} \\ { \large{ \leadsto{ \purple{ \sf{Area \: of \: circle= \: \pi r {}^{2} }}}}} \end{gathered}$

$\begin{gathered} \\ { \large{ \leadsto{ \: \: { \sf{55.44= \: \ \frac{22}{7} \: \times r {}^{2} }}}}} \end{gathered}$

• $\begin{gathered} { \large{ \underline{ \rm{By \: doing \: cross \: multiplication}}}} \end{gathered}$

$\begin{gathered} \\ { \large{ \leadsto{ \: \: { \sf{ \frac{55.44 \times 7}{22} = \: \ r {}^{2} }}}}} \end{gathered}$

$\begin{gathered} \\ { \large{ \leadsto{ \: \: { \sf{ \frac{{ \cancel{55.44 }} {}^{2.52} \times 7}{{ \cancel{22}}} = \: \ r {}^{2} }}}}} \end{gathered}$

$\begin{gathered} \\ { \large{ \leadsto{ \: \: { \sf{ 17.64 = \: \ r {}^{2} }}}}} \end{gathered}$

$\begin{gathered} \\ { \large{ \leadsto{ \: \: { \sf{ \sqrt{17.64} = \: \ r }}}}} \end{gathered}$

$\begin{gathered} \\ { \large{ \leadsto{ \: \: { \boxed{ \pink{ \mathfrak{ r = \: \ 4.2m }}}}}}} \end{gathered}$