Write the correct answer in the following: The radius of a hemisp… - Vidyadip

MCQ

Write the correct answer in the following: The radius of a hemispherical balloon increases from $6\ cm$ to $12\ cm$ as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is:

✓
$1 : 4$
B
$1 : 3$
C
$2 : 3$
D
$2 : 1$

✓

Answer

Correct option: A.

$1 : 4$

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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