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Question

(D) The initial radius $(r_1)$ of the spherical balloon is $7 \, cm$.The final radius $(r_2)$ of the spherical balloon after pumping air is $14 \, cm$

Vedclass · Accepted Answer

$1:4$

Vedclass · Answer

(D) The initial radius $(r_1)$ of the spherical balloon is $7 \, cm$.The final radius $(r_2)$ of the spherical balloon after pumping air is $14 \, cm$.The surface area of a sphere is given by the formula $A = 4 \pi r^2$.The ratio of the surface areas is given by $\frac{A_1}{A_2} = \frac{4 \pi r_1^2}{4 \pi r_2^2} = \left( \frac{r_1}{r_2} \right)^2$.Substituting the values,we get $\left( \frac{7}{14} \right)^2 = \left( \frac{1}{2} \right)^2 = \frac{1}{4}$.Therefore,the ratio of the surface areas is $1:4$.

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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