Question

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped
into it. Find the ratio of surface areas of the balloon in the two cases.​

Answer 1

$Let\:the\: initial\:Radius\:be R_{1}$

$Let\:the\:final\:Radius\:be R_{2}$

$\bold\red{\boxed{Surface\:area = \dfrac{3}{4}πr^{2}}}$

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$Surface\:area\:for\:R_{1}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×\dfrac{22}{7} × 7^{2}}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×\dfrac{22}{7} × 49}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×22 × 7}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×154}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{462}{4}}}$

$\text{Hence,the surface area of Circle with initial radius is 115.5 or }$$\dfrac{462}{4}$

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$Surface\:area\:for\:R_{2}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×\dfrac{22}{7} × 14^{2}}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×\dfrac{22}{7} × 196cm^{2}}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4}×22 × 28}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{3}{4} × 616cm^{2}}}$

$\Rightarrow\bold\blue{\boxed{Surface\:area = \dfrac{1848}{4}}}$

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ATQ

$S_{2} - S_{1}$ [S represents the surface area]

$\dfrac{1848}{4} - \dfrac{462}{4}$

$\dfrac{1386}{4}\:or\:346.5$

______________________________________$\mathcal{BE \: BRAINLY}$

Answer 2

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

$\underbrace{\bf\:For\:{1}^{st}\:case}$

$\bf\:Given:-$

• $\bf\:Radius=7\:cm$

$\rm\longrightarrow\:S.A=\:4\pi{r}^{2}$

$\rm\longrightarrow\:S.A=\:4\times\:\dfrac{22}{7}\times\:{(7)}^{2}$

$\rm\longrightarrow\:S.A=\:4\times\:\dfrac{22}{\cancel{7}}\times\:\cancel{7}\times\:7$

$\rm\longrightarrow\:S.A=\:4\times\:22\times\:7$

$\rm\longrightarrow\:S.A=\:616\:c{m}^{2}$

$\underbrace{\bf\:For\:{2}^{nd}\:case}$

$\bf\:Given:-$

• $\bf\:Radius=14\:cm$

$\rm\longrightarrow\:S.A=\:4\pi{r}^{2}$

$\rm\longrightarrow\:S.A=\:4\times\:\dfrac{22}{7}\times\:{(14)}^{2}$

$\rm\longrightarrow\:S.A=\:4\times\:\dfrac{22}{\cancel{7}}\times\:\cancel{14}\times\:14$

$\rm\longrightarrow\:S.A=\:4\times\:22\times\:2\times\:14$

$\rm\longrightarrow\:S.A=2464\:c{m}^{2}$

Now, we have

❍ $\rm\purple{{In\:first\:case,}}$

• $\rm\:S.A=616\:c{m}^{2}$

❍ $\rm\orange{{In\: second\:case,}}$

• $\rm\:S.A=2464\:c{m}^{2}$

then,

$\rm\longrightarrow\:Ratio\:of\:S.A=\dfrac{616}{2464}$

$\rm\longrightarrow\:Ratio\:of\:S.A=\dfrac{1}{4}$

$\rm\longrightarrow\:Ratio\:of\:S.A=1:4$

Hence,the ratio of surface area of balloon will be 1:4.