Gujarat BoardEnglish MediumSTD 8MATHSMensuration1 Mark
Question
Two cylinders with equal volume will always have equal surface areas.
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Answer
False. Solution:
Consider two cylinders with the following measures
e.g. $r_1 = 2\ cm, h = 9\ cm$ and $r = 3\ cm, h = 4\ cm$
For the first cylinder,
Volume $=\pi\text{r}^2\text{h}=\pi\times2^2\times9=36\pi\text{cm}^3$
Again, for the second cylinder,
Volumes $\pi\text{r}^2\text{h}=\pi\times3^2\times4$
$=36\pi\text{cm}^3$
$\therefore$ The volumes are equal.
Now, surface area of first cylinder $=2\pi\text{rh}=2\pi\times2\times9=36\pi\text{cm}^2$
and surface area of second cylinder $=2\pi\text{rh}=2\pi\times3\times4=24\pi\text{cm}^2$
which are not equal.
So, the statement is false.
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