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Surface Areas and Volumes — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSSurface Areas and Volumes1 Mark
Question
Write the correct answer in the following:
The radius of a hemispherical balloon increases from 6cm to 12cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is:
✓

Answer

  1. 1 : 4
Solution:
Balloon is hemispherical in shape.
Surface area of hemispherical balloon of radius is $=2\pi\text{r}^2$
Now, $\frac{\text{S}_1}{\text{S}_2}=\frac{2\pi\text{r}^2_1}{2\pi\text{r}^2_1}=\frac{\text{r}^2_1}{\text{r}^2_2}=\frac{(6)^2}{(12)^2}=\frac{36}{144}=1:4$
Therefore, the ratio of the surface areas of two balloons = 1 : 4
Hence, (a) is the correct answer.

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