Question

A hexagonal hole of each side 2 metres is dug in the school ground to collect rain water. It is 3 metres deep. It now has water one metres deep.how much litres of water is there in it?

Answer 1

There are 10392.3 litres of water in the hexagonal hole of the school ground.

Step-by-step explanation:

It is given that,

The side of the hexagonal hole, a = 2 m

The depth or height of the hole, h = 3 m

The level of water in the hole, l = 1 m

In order to find the litres of water-filled in the hole, we need to find the volume of the hexagonal hole occupied by water in litres.

So,  

[The volume of water] = [The level of water in hole] * [Area of the base of the hexagonal base]

Substituting the given values, we get

⇒ The volume of water = 1 × $3\frac{\sqrt{3}}{2}$ × side²

⇒ The volume of water = $3*\frac{\sqrt{3}}{2}$ × 2²  

⇒ The volume of water = $3 * \frac{\sqrt{3}}{2}$ × 4  

⇒ The volume of water = 10.3923 m³

We know that 1 m³ = 1000 litres.

∴ The volume of water in the hole in litres is,

= 10.3923 m³ * 10³ L

= 10392.3 L

Thus, 10392.3 litres of water is there in the hexagonal hole of the school ground.

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Answer 2

Answer:

The amount of water in the hole is: 10392 liters

Step-by-step explanation:

To get the volume of the water, we must first get the capacity of the hole.

The volume of the hexagonal hole is given by:

Volume = Base area × height

To get the area of the hexagon, we need to find the height of the six equilateral triangles of side 2 meters.

Using Pythagorean theorem we have:

√2²- 1² = √3 = height

Area of triangle = 1/2 × base × height

Applying this we have: 1/2 × 2 × √3 = √3 m²

We have six triangles, so the total area of the hexagon = √3 × 6 = 6√3 m²

Since the water is 1 meter deep, the volume of the water is given by:

6√3 × 1 = 10.392 m³

We need to convert this to liters.

We have that:

1 cubic meter = 1000 liters.

So, we have : 1000 × 10.392 = 10392 liters