Question

A military tent of height $8.25$ m 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 canvas used in making the tent, if the breadth of the canvas is $1.5m.$

Answer 1

Given,

Height of the military tent $=8.25m$

Height of the circular cylinder $4=5.5m$

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

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

Therefore, height of the right circular cone $=2.75m$

We know that,

Slant height of the cone(l)= $\sqrt{h^2+r^2}$

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

radius of cylinder = radius of cone

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

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

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

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

​Slant height, $l=15.25m$

Surface area of cone= $\pi \times r\times l$ $=3.14\times 15\times 15.25=718.3$

Surface area of cylinder = 2$\pi \times r\times h$ $=2\times 3.14\times 15\times 5.5=518.1$

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

$=718.9+518.57$

$=1236.47m^2$

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