Question

If the volume of a cylinder is $3080{\text{cm}}^3$ and the base radius is $7$ cm, find the total surface area of the cylinder.

Answer 1

Let the height be $h.$

Volume of the cylinder $=3080$cm

Radius $=7$cm

$\pi =\frac{22}{7}$

Volume of cylinder $=3080$

$\pi r^{2}h=3080$

$\Rightarrow \frac{22}{7}\times 7\times 7\times h=3080$

$\Rightarrow 154\times h=3080$

$\Rightarrow h=\frac{3080}{154}$

$\Rightarrow h=20cm$

Totals surface area of the cylinder.

$=2\pi rh+2\pi r^2$

$=2\cdot \frac{22}{7}\cdot 7\cdot 20+2\cdot \frac{22}{7}\cdot 7\cdot 7$

$=2\cdot 440+44\cdot 7$

$=880+308$

$=11,880$cm.