Question

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Answer 1

Hint: We need to calculate the volume of the bowl as the amount of milk that can be held in the bowl is equal to the bowl's capacity.
And Capacity= Volume of the bowl.
We will use the formula for volume of hemisphere as the bowl is in the shape of a hemisphere (given)
Volume of hemi-sphere = $2/3\pi {r^3}$

Complete step-by-step answer:
Diameter of the hemisphere= 10.5 cm
Radius ,
$
 r = {\text{ }}10.5/2cm \\
   = {\text{ }}5.25cm \\
 $ (as radius = Diameter/2)
 

Now,
Volume of Hemispherical bowl= $2/3\pi {r^3}$
Substituting the value of r, we get:
\[2/3\pi {r^3} = (2/3)\pi {(5.25)^3}\]
\[
   = (2/3)(22/7) \times 5.25 \times 5.25 \times 5.25 \\
   = (2/3)(22/7)(525/100)(525/100)(525/100) \\
 \]
\[ = 303.1875\]cm3

Converting into litres:
\[ = 303.1875*(1/1000)\]
\[ = 0.3031875\] (As 1 cm3 = 1 ml, ∴1 cm3= 1/1000 l)


Note: Be Careful of the units, volume is generally measured in litres, this is why we made appropriate conversions so that the unit of volume obtained will be litres. In simple terms volume is nothing but the space that is enclosed by any three dimensional object. Make conversions wherever necessary in any mensuration problem. Remember
1 m³= 1000 l and 1cm³ = 1 ml