Answer:
The problem is all about volumes.
The volume of a hemisphere is defined as
[tex]V=\frac{2}{3} \pi r^{3}[/tex]
According to the problem
[tex]d_{outside}=44.6cm[/tex]
[tex]d_{inside}=41.6cm[/tex]
Using the definition of radius
[tex]r_{outside}=\frac{44.6cm}{2}=22.3cm[/tex]
[tex]r_{inside}=\frac{41.6cm}{2}=20.8cm[/tex]
Now, the volume of the inside bowl is
[tex]V_{inside}=\frac{2}{3}\pi(20.8cm) ^{3} \approx 5999.27 (3.14) \ cm^{3} \approx 18837.71 \ cm^{3}[/tex]
Therefore, the bowl can have 18,837.71 cubic centimeters of soup. (A)
The volume of the clay needed can be found with the differnece between hemispheres.
[tex]V_{clay}=V_{outside} -V_{outside}[/tex]
[tex]V_{clay}=\frac{2}{3}(3.14)(22.3cm)^{3}-18837.71cm^{3}= 23214.16 cm^{3}-18837.71cm^{3}= 4376.45 \ cm^{3}[/tex]
Therefore, we needed 4376.45 cubic centimeters of clay to make a single bowl. (B)
At last, the space that a single bowl occupies in the box is
[tex]V_{outside}=23214.16 \ cm^{3}[/tex]
If we have 6 bowls, the total volume is
[tex]V_{total}=6(23214.16 \ cm^{3} )= 139284.96 \ cm^{3}[/tex]
Now, we need to find the volume of the box
[tex]V_{box}=22.5cm \times 90cm \times 135 cm = 273375cm^{3}[/tex]
The empty space between the box and the 6 bowls is
[tex]V_{sawdust}=V_{box} - V_{total}=273375 cm^{3}-139284.96 cm^{3} =134090.04cm^{3}[/tex]
This empty space volume represents the sawdust packing needed, because the function of it is to fill the empty space.
Therefore, we need 134090.04 cubic centimeters of sawdust packing. (C)
