Question

The height of a conical tent is $14m$ and its floor area is $346.5m^2$. The length of canvas, $1.1m$ wide, required for it is:

• A. $490m$
• B. $525m$
• C. $665m$
• D. $860m$

Answer 1

The correct option is B $525m$

Surface area of the base $=\pi r^2=346.5\Rightarrow r^2=(\frac{3465}{10}\times \frac{7}{22})$
$=\frac{441}{4}=(\frac{21}{2}{)}^2\Rightarrow r=\frac{21}{2}m$
$l=\sqrt{r^2+h^2}=\sqrt{\frac{441}{4}+(14{)}^2}=\sqrt{\frac{1225}{4}}=\frac{35}{2}m$
$Areaofcanvas=\pi rl$
$=(\frac{22}{7}\times \frac{21}{2}\times \frac{35}{2})m^2=577.5m^2$
$Lengthofcanvas=\frac{Area}{Width}=\frac{557.50}{1.1}m=525m$.