Question

A tent of height 77 dm is in the form a right circular cylindrer of diameter 36 m and height 44 dm surrounded by a right circular cone. Find the cost of the canvas at Rs.3.50 per m^2.

Answer 1

Given:

Diameter of base = 36 m

$=>Radiusofbase\left(r\right)=\frac{36}{2}=18m$

$heightofcylinder\left(H\right)=44dm=\frac{44}{10}=4.4Mm$

$andtotalheight=77dm=\frac{77}{10}=7.7m$

Thus height of cone (h) = 7.7 m – 4.4 m = 3.3 m

$Alsoslantheight\left(l\right)=\sqrt{r^2+h^2}=\sqrt{{18}^2+{3.3}^2}=\sqrt{324+10.89}=\sqrt{334.89}=18.3m$

Now C.S.A. of tent = C.S.A. of cylinder + C.S.A. of cone

$=2\pi rH+\pi rl=\pi r(2H+l)$

$\frac{22}{7}\times 18(2\times 4.4+18.3)m^2$

$\frac{396}{7}\left(27.1\right)=\frac{10731.6}{7}{m}^2$

also cost of $1m^2$ Canvas = Rs 3.50

$Costoftotalcanvas=Rs.3.50\times \frac{10731.6}{7}=Rs.5365.80$