Question

A military tent of height $8.25m$ is in the form of a right circular cylinder of base diameter $30m$ and height $5.5m$ surmounted by a right circular cone of same base radius. Find the length of the canvas use in making the tent, if the breadth of the canvas is $1.5m$.

Answer 1

Height of the military tent = Height of the circular cylinder + Height of the right circular cone

Given,

Height of the military tent = $8.25m$

Height of the circular cylinder $=5.5m$

Height of the right circular cone $=8.25-5.5$

therefore Height of the right circular cone = $2.75m$

We know that,

The slant height of a cone, $l=\sqrt{(r^2+h^2)}$

where, $r=$ radius of base and $h=$ altitude height of cone

radius of cylinder = radius of cone

therefore radius of cone$=\frac{30}{2}=15m$

$l=\sqrt{(r^2+h^2)}$

$l=\sqrt{({15}^2+{2.75}^2)}$

$l=\sqrt{(225+7.5625)}$

slant height, $l=15.25m$

Surface area of cone $=\pi rl=\pi \times 15\times 15.25=718.9m$

Surface area of cylinder $=2\pi rh=2\times \pi \times 15\times 5.5=518.57m$

Area of the canvas $=$ Surface area of cone $+$ Surface area of cylinder

$=718.9+518.57$

$=1236.47m^2$

$\therefore$ Length of canvas $=\frac{1236.47}{1.5}=824.3m$