Question

The volume of acylinder is 308cmcube.its height is 8cm.find its later surface area and total surface area

Answer 1

$volume = {308cm}^{3}$
Height = 8cm.....
We know,
$volume \: of \: a \: cylinder \: = \pi {r}^{2} h \\ = > {308cm}^{3} = \frac{22}{7} \: cm\times {r}^{2} \times 8cm \\ = > {r}^{2} = \frac{ {308cm}^{3} \times 7}{22cm \times 8cm} \\ = > {r}^{2} = \frac{49}{4} cm \\ = > r = \sqrt \frac{49}{4} cm \\ = > r = \frac{7}{2}cm = 3.5cm$
Therefore, r=3.5cm....
Now, CSA/LSA(Curver/Lateral Surface Area)=
$2\pi rh \\ = (2 \times \frac{22}{7} \times \frac{7}{2} \times 8) {cm}^{2} \\ = 176 {cm}^{2}$
And TSA(Total Surface Area)=
${2\pi rh(csa) + \pi {r}^{2} } \\ = 176 {cm}^{2} + (\frac {22 \times 7 \times 7}{7 \times 2 \times 2 } ) {cm}^{2} \\ = (176 + 38.5) {cm}^{2} \\ = 214.5 {cm}^{2}$
THERE YOU GO!!!.....