The radius of a hemispherical balloon increas | vedclass

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(C) The balloon is hemispherical in shape.The surface area of a hemispherical balloon with radius $r$ is given by the formula $S = 3\pi r^2$.Let $r_1

Vedclass · Accepted Answer

$1:4$

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(C) The balloon is hemispherical in shape.The surface area of a hemispherical balloon with radius $r$ is given by the formula $S = 3\pi r^2$.Let $r_1 = 6\,cm$ and $r_2 = 12\,cm$ be the radii in the two cases.The ratio of the surface areas is $\frac{S_1}{S_2} = \frac{3\pi r_1^2}{3\pi r_2^2} = \frac{r_1^2}{r_2^2}$.Substituting the values,we get $\frac{S_1}{S_2} = \frac{6^2}{12^2} = \frac{36}{144} = \frac{1}{4}$.Therefore,the ratio of the surface areas of the two balloons is $1:4$.

The radius of a hemispherical balloon increases from $6\,cm$ to $12\,cm$ as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is

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