Question

The radius of a spherical balloon increase from 7cm to 14 cm as air is being pumped into it .find the ratio of the surface are of the balloon in the two case.​

Answer 1

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Answer 2

$\bf{\underline{\red{Correct\:Question:-}}}$

✓✓The radius of a spherical balloon increase from 7cm to 14 cm as air is being pumped into it .find the ratio of the surface are of the balloon in the two case.

$\bf{\underline{\green{Solution:-}}}$

$\bf\boxed\star\pink{\underline{\underline{{For\:first\:case}}}}:-$

$\bf\:Given:-$

• $\bf\:Radius=7\:cm$

$\bf\implies\:S.A=\:4π{r}^{2}$

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

$\bf\implies\:S.A=\:4\times\:\dfrac{22}{7}\times\:7\times\:7$

$\bf\implies\:S.A=\:4\times\:22\times\:7$

$\bf\implies\:S.A=\:616\:c{m}^{2}$

$\bf\boxed\star\blue{\underline{\underline{{For\: second\:case}}}}:-$

$\bf\:Given:-$

• $\bf\:Radius=14\:cm$

$\bf\implies\:S.A=\:4π{r}^{2}$

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

$\bf\implies\:S.A=\:4\times\:\dfrac{22}{7}\times\:14\times\:14$

$\bf\implies\:S.A=\:4\times\:22\times\:2\times\:14$

$\bf\implies\:S.A=2464\:c{m}^{2}$

Now, we have

❍ $\bf\purple{{In\:first\:case,}}$

• $\bf\:S.A=616\:c{m}^{2}$

❍ $\bf\orange{{In\: second\:case,}}$

• $\bf\:S.A=2464\:c{m}^{2}$

then,

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

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

$\bf\:Ratio\:of\:S.A=1:4$

[Here, S.A indicates Surface area]