(a) height is doubled |
(b) height is doubled and the radius is halved |
(c) height remains same and the radius is halved. |
Answer:
Volume of cylinder \[=\pi {{r}^{2}}h\] (a) Height is doubled i.e., h' =2h Volume of cylinder \[=\pi {{r}^{2}}h'\] \[=\pi {{r}^{2}}(2h)\] \[=2\pi {{r}^{2}}h\] (Double of the original) (b) \[h'=2h\]and\[r'=\frac{r}{2}\] Then volume of cylinder \[=\pi {{r}^{2}}h\] \[=\pi {{\left( \frac{r}{2} \right)}^{2}}\times 2h\] \[=\pi \,\times \frac{{{r}^{2}}}{4}\times 2h\] \[=\frac{1}{2}\pi {{r}^{2}}h\] (Half of the original) (c) \[r'=\frac{r}{2}\] unit Volume of cylinder \[=\pi r{{'}^{2}}h\] \[=\pi \,{{\left( \frac{r}{2} \right)}^{2}}h\] \[=\frac{1}{4}\pi {{r}^{2}}h\]cubic unit (One fourth of the original)
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