Question
A solid cylinder has a total surface area of $462\ cm^2$. Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.
✓
Answer
Given that Curved or lateral surface area $= 13 \times $ total surface area
$2\pi\text{rh}=\frac{1}{3}(2\pi\text{rh}+2\pi\text{r}^2)$
$4\pi\text{rh}=2\pi\text{r}^2$
$2\text{h}=\text{r}$ Total surface area $= 462cm^2$
Curved surface area $=\frac{1}{3}\times462$
$2\pi\text{rh}=154$
$2\times3.14\times2\times\text{h}^2=154$
$\text{h}^2=\frac{49}{4}$
$\text{h}=\frac{49}{4}\text{cm}$
$=\frac{7}{2}\text{cm}$
Now $r = 2h$
Therefore $\text{r}=2\times\text{7}{2}\text{cm}=7\text{cm}$
The height and the radius of the cylinder is $\frac{7}{2}\text{cm}$ and $7cm$ respectively.
$2\pi\text{rh}=\frac{1}{3}(2\pi\text{rh}+2\pi\text{r}^2)$
$4\pi\text{rh}=2\pi\text{r}^2$
$2\text{h}=\text{r}$ Total surface area $= 462cm^2$
Curved surface area $=\frac{1}{3}\times462$
$2\pi\text{rh}=154$
$2\times3.14\times2\times\text{h}^2=154$
$\text{h}^2=\frac{49}{4}$
$\text{h}=\frac{49}{4}\text{cm}$
$=\frac{7}{2}\text{cm}$
Now $r = 2h$
Therefore $\text{r}=2\times\text{7}{2}\text{cm}=7\text{cm}$
The height and the radius of the cylinder is $\frac{7}{2}\text{cm}$ and $7cm$ respectively.
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