Question

A tent is in the form of a right circular cylinder surmounted by a cone.The diameter of cylinder is 24 m.The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground.Find the area of the canvas required for the tent.

Answer 1

Diameter of the cylindrical portion = 24 m

$\therefore Radius\left(r\right)=\frac{24}{2}=12m$

Height of cylindrical portion=11 m

and total height= 16 m

$\therefore Heightofconicalportion=16-11=5m$

$\therefore Slantheightoftheconicalportion\left(l\right)=\sqrt{r^2+h^2}=\sqrt{(12{)}^2+(5{)}^2}=\sqrt{144+25}=\sqrt{169}=13mNowareaofcanvasusedinit=2\pi rh+\pi rl=\pi r(2h+l)=\frac{22}{7}\times 12(2\times 11+13)m^2=\frac{264}{7}(22+13)=\frac{264}{7}\times 35m^2=1320m^2$