Question

The depth of hemispherical water is 2.1 m at the centre find the capacity of the water tank in liters.

Answer 1

Hemispherical water tank means it should have the volume half of the total sphere

The depth is from the Centre thus it can be stated as the radius of sphere i.e. r= 2.1 m

Volume of hemispherical tank = ½×4/3 pi r³

_____________= 2/3× 22/7 × 2.1³ m³

___________= 19.3961 m³

Now I m³ = 1000 litre
So 19.3961 m³ = 19396.1 litre.
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Hope this is ur required answer.
Proud to help you dear.

Answer 2

The capacity of the water tank in litres is 19404 litres.

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Let's understand a few concepts:

To find the capacity of the given hemispherical water tank we will use the following formula for calculating the volume of a hemisphere:

$\boxed{\bold{Volume\:of\:hemisphere = \frac{1}{2}\times Volume\:of\:sphere = \frac{1}{2}\times \frac{4}{3}\pi r^3= \frac{2}{3}\pi r^3 }}$

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Let's now solve the given problem:

The depth of the water in the hemispherical tank at the centre = 2.1 m

So, we can say that,

The depth of the hemispherical water tank at the centre = Radius of the tank (r) = 2.1 m

By using the formula of the volume of the hemisphere, we get

The capacity of the hemispherical water tank is,

= Volume of hemispherical water tank

= $\frac{2}{3}\pi r^3$

= $\frac{2}{3}\times \frac{22}{7} \times 2.1^3$

= $\frac{2}{3}\times \frac{22}{7} \times 2.1 \times 2.1 \times 2.1$

= $\frac{2\times 22}{21}\times 2.1 \times 2.1 \times 2.1$

= $2\times 22\times 0.1 \times 2.1 \times 2.1$

= $19.404\:m^3$

now to get the final required answer we will convert m³ into litres using the conversion rate of $\boxed{\bold{1\:m^3= 1000\: litres}}$

= $19.404\times 1000\:litres$

= $\bold{19404\:litres}$

Thus, the capacity of the water tank in litres is 19404 litres.

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