Question

Find what length of canvas,1.5 m in width is required to make a conical tent 48 m in diameter and 7 m in heigh ? Given that 10% of canvas is used in stitchings. Also find cost of canvas at a rate of Rs.24 per meter.

Answer 1

width of canvas $=1.5m$

Diameter of tent to bemade $=48m$

$\Rightarrow$ Radius $=24m$

and height $7m$

$\Rightarrow$ Slant height $\left(l\right)=\sqrt{h^2+r^2}=\sqrt{7^2+{24}^2}=25m$

Now curved surface area $=\pi rl$

$=\frac{22}{7}\times 24\times 25=1885.71m^2$

But only $1$% allowance for folds and stiching

Hence new areas $=1885.71m^2+\frac{10}{100}\times 1885.71m^2$

$=2074.28m^2$

Width of canvas $=1.5m$

Length of canvas $=\frac{Area}{width}=\frac{2074.28m^2}{1.5m}$

$=1382.85m$

Now cost of $1m=Rs.24$

Total cost $=Rs.24\times 1382.85=Rs.33188.4$