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How many litres of water will a hemispherical tank hold whose diameter is $ 4.2m $ ?

Last updated date: 23rd May 2024
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Hint: First of all find the volume of the hemispherical tank and since measure of diameter is in meter first convert it in radius and resultant volume would be cubic meter and then at last convert the meter cube in liters.

Complete step-by-step answer:
Given that: Diameter, $ d = 4.2m $
We know that radius is half of the diameter.
 $ \therefore r = \dfrac{d}{2} $
Place value and simplify –
 $ \therefore r = \dfrac{{4.2}}{2} = 2.1m $
Volume of the hemispherical tank is given by $ V = \dfrac{2}{3}\pi {r^3} $
Place values in the above equation –
 $ V = \dfrac{2}{3} \times \left( {\dfrac{{22}}{7}} \right) \times {\left( {2.1} \right)^3} $
Simplify the above equation –
 $ V = \dfrac{2}{3} \times \left( {\dfrac{{22}}{7}} \right) \times \left( {2.1} \right) \times \left( {2.1} \right) \times \left( {2.1} \right) $
Common factors from both the denominator and the numerator cancel each other,
 $ V = 2 \times \left( {22} \right) \times \left( {0.1} \right) \times \left( {2.1} \right) \times \left( {2.1} \right) $
Simplify the above expression finding the product of the terms –
 $ V = 19.404{m^3} $ ….. (A)
Convert cubic metre in litres.
 $ 1{m^3} = 1000{\text{ }}litres $
Use equation (A) and convert it in litres-
   \Rightarrow V = 19.404 \times 1000{\text{ litres}} \\
   \Rightarrow V = 19404\;litres \;
Hence, the hemispherical tank can hold $ 19404 $ liters of water.
So, the correct answer is “ $ 19404 $ liters of water.”.

Note: The most important here is the standard formula and application and also its simplification. Always remember the basic conversion relations and convert as per the need. Meter cube to litres and centimetre cube in liters. Remember the difference among the units such as one meter and one centimetre both gives us the measure of length. Remember all the formulas for the volume and area for the closed and open figures. Know the difference between the volume and the areas of the figures. Volume is measured in cubic units and the area is measured in the square units.