Question

A military tent is in the form of a circular cone of
vertical height 6 m, the diameter of the base being
7 m. If 12 soldiers can sleep in it, find the average
cubic metre of air space required per soldier.​

Answer 1

Answer: ≈ 6.42 m³

A military tent is in the form of a circular cone of vertical height, h = 6 m. The diameter of the base being, d = 7 m

It is given that, 12 soldiers can sleep in it, and we need to find the average cubic metre of air space required per soldier.

For finding the average volume of air space required per soldier. We should find the volume of the tent and divide it by 12 because there are 12 soldiers in the tent.

Tent,

• Height, h = 6 m
• Radius, r = d/2 = 7/2 m

We know,

▶ Volume of Cone = 1/3.π.r².h

[ Put π = 22/7 ]

⇒ Volume of Tent = 1/3 . 22/7 . 7/2 . 7/2 . 6

⇒ Volume of Tent = 1/3 . 22 . 1/2 . 7/2 . 6

⇒ Volume of Tent = 1/3 . 11 . 7/2 . 6

⇒ Volume of Tent = 1/3 . 11 . 7 . 3

⇒ Volume of Tent = 11 . 7

⇒ Volume of Tent = 77 m³

Now, As we have discussed earlier:

⇒ Volume required per Solider = Volume/12

⇒ Volume required per Soldier = 77/12

⇒ Volume required per Soldier ≈ 6.42 m³

Hence, Volume of air space required per soldier is 6.42 m³ approx.

Answer 2

Answer:

Given :-

• A military tent is in the form of a circular cone of vertical height is 6 m, the diameter of the base being 7 m.
• If 12 soldiers can sleep in it.

To Find :-

• What is the average cubic metre of air space required per soldiers.

Formula Used :-

➲ Volume of Cone = 1/3πr²h

where,

• r = Radius
• h = Height

Solution :-

First, we have to find the radius a circular cone :

We know that,

➲ Radius = Diameter/2

Then,

Given :

• Diameter = 7 m

According to the question by using the formula we get,

↦ Radius = 7/2

➦ Radius = 3.5 m

Now, we have to find the volume of a circular cone,

Given :

• Height = 6 m
• Radius = 3.5 m

According to the question by using the formula we get,

➡ Volume of circular cone :

⇒ 1/3 × 22/7 × (3.5)² × 6

⇒ 1/3 × 22/7 × 3.5 × 3.5 × 6

⇒ 1/3 × 22/7 × 12.25 × 6

⇒ 22/7 × 12.25 × 2

⇒ 22/7 × 24.5

➠ 77 m³

Hence, the volume of circular cone is 77 m³.

Now, we have to find the average cubic metre of air space required per soldiers,

As we know that,

➲ The average cubic metre of air space required per soldiers = Volume of circular cone/Total soldiers

Given :

• Volume of circular cone = 77 m³
• Total soldiers = 12

According to the question by using the formula we get,

⇒ The average cubic metre of air space required per soldiers,

⇒ 77/12

➦ 6.42 m³

∴ The average cubic metre of air space required per soldiers is 6.42 m³.