A military tent is in the form of a right circular cone of vertical height 6 m ,the diameter of the base being 7 m . if 12 soilder can sleep in it . find the average cubic metres of air space required per soilder.
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Answers
Given :-
• A military tent is in the form of right circular cone.
• The height of the cone is 6m
• The base diameter of the cone is 7m
Solution :-
Here,
A military tent is in the form of right circular cone
We know that,
Total surface area of right circular cone
= πrl + πr²
Radius of the cone = 7/2 = 3.5
Slant height of the cone
l² = h² + r²
l² = (6)² + ( 3.5)²
l² = 36 + 12.25
l = √48.25
l = 6.94
Thus, The slant height of the cone is 6.94m
Now
Subsitute the required values in the given formula ,
= 22/7 * 7/2 * 6.94 + 22/7 * 7/2 * 7/2
= 11 * 6.94 + 11 * 7/2
= 11 * 6.94 + 11 * 3.5
= 76.34 + 38.5
= 114.84m²
Thus, The area of the right circular cone is 117.84m²
Now,
It is given that in a single tent 12 soldiers can sleep in it. so, now we have to find the area covered by 1 solider
Therefore,
Area covered by one soldier
= 114.84/12
= 9.57m²