Question
A rectangular sheet of dimensions $25\ cm \times 7\ cm$ is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.
✓
Answer
A rectangular sheet of demensions $25\ cm \times 7\ cm$ is rotated about its longer side which makes a cylinder with base $25\ cm$ and height $7\ cm$.
Surface area of a base $=2\pi\text{r}$
$\therefore2\pi\text{r}=25\text{cm}$
$\Rightarrow\text{r}=\frac{25\times7}{2\times22}=\frac{175}{44}\text{cm}$
Volume of a cylinder $=\pi\text{r}^2\text{h}$ $=\frac{22}{7}\times\frac{175}{44}\times\frac{175}{44}\times7$
$=\frac{175\times175}{2\times44}=\frac{30625}{88}$
$=348.011\text{cm}^3$
Surface area $=2\pi\text{rh}=2\times\frac{22}{7}\times\frac{175}{44}\times7$
$=\frac{44}{44}\times175$ $=175\text{cm}^2$
Surface area of a base $=2\pi\text{r}$
$\therefore2\pi\text{r}=25\text{cm}$
$\Rightarrow\text{r}=\frac{25\times7}{2\times22}=\frac{175}{44}\text{cm}$
Volume of a cylinder $=\pi\text{r}^2\text{h}$ $=\frac{22}{7}\times\frac{175}{44}\times\frac{175}{44}\times7$
$=\frac{175\times175}{2\times44}=\frac{30625}{88}$
$=348.011\text{cm}^3$
Surface area $=2\pi\text{rh}=2\times\frac{22}{7}\times\frac{175}{44}\times7$
$=\frac{44}{44}\times175$ $=175\text{cm}^2$
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