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Surface Areas and Volumes — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Areas and Volumes1 Mark
MCQ
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:
  • A
    1 : 4
  • B
    1 : 3
  • C
    2 : 3
  • D
    2 : 1
✓

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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