Question

How many liters of milk can a hemispherical bowl of diameter \[10.5\text{ }cm\] hold?

Answer 1

Hint: To find the volume of any object especially in case of spherical (full or half) we need the radius or diameter of the object. And to know the amount of substance filled in the object in terms of the volumetric unit we need to find the volume of the object in terms of radius or diameter. To find the volume of the liquid that a hemispherical bowl can hold we use:
Volume of the bowl \[=\dfrac{2}{3}\pi {{r}^{3}}\]
where \[r=\dfrac{d}{2}\] meaning \[r\] is the radius and \[d\] is the diameter both in same dimensions and the value of \[\pi =3.14\].

Complete Step-by-step Solution
Now placing the value of radius as \[r=\dfrac{d}{2}\]
\[r=\dfrac{10.5\text{ }cm}{2}\]
\[=5.25\text{ }cm\]
We get the volume of the liquid filled in the hemispherical bowl as:
\[=\dfrac{2}{3}\pi {{r}^{3}}\]
\[=\dfrac{2}{3}\pi {{\left( 5.25 \right)}^{3}}\]
\[=303.1875\text{ }c{{m}^{3}}\]
Now to convert the volume from \[c{{m}^{3}}\] to \[litres\] we use:
\[303.1875\text{ }c{{m}^{3}}\times \dfrac{1}{1000}\] …(as \[1\text{}c{{m}^{3}}=\dfrac{1}{1000}litres\])
\[=0.303\text{ }litres\]

Hence, the volume of the liquid filled in the hemispherical bowl is \[0.303\text{ }litres\].

Note:
Students may go wrong during the conversion of \[c{{m}^{3}}\] to \[litres\] as the conversion is a two set process meaning the volume is first needed to be converted into \[millilitres\] and then into \[litres\] as:
\[1c{{m}^{3}}=1millilitres\].
\[1millilitres=\dfrac{1}{1000}litres\].
\[1c{{m}^{3}}=\dfrac{1}{1000}litres\].