Question

Find the lateral surface area and the total surface area of a solid cylinder of height 14 cm, if its volume is $686\pi c{m}^3$

• A.
  CSA= $614c{m}^2$ and TSA= $756c{m}^2$
• B.
  CSA= $616c{m}^2$ and TSA= $924c{m}^2$
• C.
  CSA= $233c{m}^2$ and TSA= $798c{m}^2$
• D.
  CSA= $614c{m}^2$ and TSA= $773c{m}^2$

Answer 1

The correct option is B

CSA= $616c{m}^2$ and TSA= $924c{m}^2$

Let the radius of a cylinder be 'r' cm
height = h = 14 cm
Volume = $686\pi c{m}^3$
$\Rightarrow \pi r^{2}h=686\pi c{m}^3$
$\Rightarrow r^2\times 14=686\Rightarrow r^2=\frac{686}{14}$
$\Rightarrow \sqrt{r^2}=\sqrt{49}\Rightarrow r=7cm$
Curved / Lateral surface area = $2\pi rh=2\times \frac{22}{7}\times 7\times 14$
=$616c{m}^2$
Total surface area
= $2\pi r(h+r)=2\times \frac{22}{7}\times 7(14+7)$
=$924c{m}^2$