Question

The Radius of a Spherical balloon increases from 7 cm to 14 cm as air is pumped inside it .Find the ratio of Surface Areas in both cases .​

Answer 1

Answer:

1: 4

1: 4It is given that radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. We have found that the ratio of the surface areas of the balloons in the two cases is 1: 4.

Step-by-step explanation:

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Answer 2

Given :

• The Radius of a Spherical balloon increases from 7 cm to 14 cm .

To Find :

• Find the Ratio of Surface Areas

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SolutioN :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Surface \; Area {\small_{(Sphere)}} = 4 \pi {r}^{2} }}}}}$

$\maltese$ Calculating the Ratio :

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{Surface \; Area \; of \; Old \; Balloon}{Surface \; Area \; of \; New \; Balloon} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{4 \times \pi \times {r}^{2} }{4 \times \pi \times {r}^{2}}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{4 \times \pi \times {7}^{2} }{4 \times \pi \times {14}^{2}}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{ \cancel4 \times \pi \times {7}^{2} }{ \cancel4 \times \pi \times {14}^{2}}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{ \pi \times {7}^{2} }{ \pi \times {14}^{2}}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{ \cancel{\pi} \times {7}^{2} }{ \cancel{\pi} \times {14}^{2} }} \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{ {7}^{2} }{ {14}^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{ 49 }{ 196 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \cancel\dfrac{ 49 }{ 196 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Ratio = \dfrac{ 1 }{ 4 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Ratio = 1:4 }}}}} \; {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Ratio of Surface Areas is both cases is 1:4 .

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