Answer:
Part 1) Option a. [tex]240\ dices[/tex]
Part 2) Option c. [tex]9.156.24\ pounds[/tex]
Step-by-step explanation:
Part 1)
step 1
Find the volume of one dice
The volume is equal to
[tex]V=b^{3}[/tex]
we have
[tex]b=2\ cm[/tex]
substitute
[tex]V=2^{3}=8\ cm^{3}[/tex]
step 2
Find the volume of the box
The volume is equal to
[tex]V=LWH[/tex]
we have
[tex]L=20\ cm[/tex]
[tex]W=12\ cm[/tex]
[tex]H=8\ cm[/tex]
substitute
[tex]V=20*12*8=1,920\ cm^{3}[/tex]
step 3
Find the number of dices
Divide the volume of the box by the volume of one dice
[tex]1,920/8=240\ dices[/tex]
Part 2)
step 1
Find the volume of the cylinder
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=9\ ft[/tex]
[tex]h=12\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=(3.14)(9)^{2}(12)[/tex]
[tex]V=3,052.08\ ft^{3}[/tex]
step 2
Find how many pounds of sand will fit into the cylinder
using proportion
[tex]\frac{3}{1}\frac{pounds}{ft^{3}}=\frac{x}{3,052.08}\frac{pounds}{ft^{3}}\\ \\x=3,052.08*3\\ \\x=9.156.24\ pounds[/tex]
