# A right cylinder has a circumference of 16π cm. Its height is half the radius. What is the lateral area and the surface area of the cylinder rounded to the nearest tenth?

Aug 4, 2018

color(green)(L S A " of cylinder " = 2 pi r h = 64pi ~~ 201.1cm^2

color(chocolate)(T S A = L S A + A_(tb) = 64pi + 128 pi = 192 pi ~~ 603.2 cm^2

#### Explanation:

$\text{Circumference } = C = 2 \pi r = 16 \pi c m$

$r = \frac{16}{2} = 8 c m$

$\text{Height } h = \frac{r}{2} = \frac{8}{2} = 4 c m$

$\text{Lateral Surface Area of cyl. } L S A = 2 \pi r h = 2 \pi \cdot 8 \cdot 4 = 64 \pi c {m}^{2} \approx 201.1 c {m}^{2}$

$\text{Top+Bottom Area of cyl} = {A}_{t b} = 2 \pi {r}^{2} = 2 \pi {8}^{2} = 128 \pi c {m}^{2}$

$\text{Total Surface Area of cyl} = T S A = L S A + {A}_{t b}$

$T S A = 64 \pi + 128 \pi = 192 \pi \approx 603.2 c {m}^{2}$