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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.

Q : 4    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.

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Given,

r_1 = 7\ cm

r_2 = 14\ cm

We know,

The surface area of a sphere of radius r = 4\pi r^2

\therefore The ratio of surface areas of the ball in the two cases = \frac{Initial}{Final} = \frac{4\pi r_1^2}{4\pi r_2^2}

= \frac{r_1^2}{r_2^2}

\\ = \left (\frac{7}{14} \right )^2 \\ \\ = \left (\frac{1}{2} \right )^2 \\ \\ = \frac{1}{4}

Therefore, the required ratio is 1:4

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