Part A
To show the total capacity of container B is 132 cm³
volume = unit rate × time taken
volume = 6 cm³ × 22
volume = 132 cm³ ∴ Hence proved.
Find radius
[tex]\sf volume \ of \ cone = \dfrac{1}{3} \pi r^2 h[/tex]
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[tex]\rightarrow \sf \dfrac{1}{3} * \dfrac{22}{7} * r^2 * 14 = 132[/tex]
simplify
[tex]\rightarrow \sf \dfrac{44}{3} * r^2= 132[/tex]
change sides
[tex]\rightarrow \sf r^2= \dfrac{132(3)}{44} = 9[/tex]
square root both sides
[tex]\rightarrow \sf r = 3[/tex]
∴ Hence the radius of cone (Shape B is 3 cm)
To show the time taken
volume = unit rate × time taken
[tex]\sf volume \ of \ hemi -sphere = \dfrac{2}{3} \pi r^3[/tex]
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[tex]\sf \rightarrow \dfrac{2}{3} \pi r^3 = 6 * time \ taken[/tex]
Insert values
[tex]\sf \rightarrow \dfrac{2}{3} *\dfrac{22}{7} \ r^3 = 6 * time \ taken[/tex]
exchange sides
[tex]\sf \rightarrow time \ taken = \dfrac{2}{3} *\dfrac{22}{7} \ r^3 *\dfrac{1}{6}[/tex]
simplify following
[tex]\sf \rightarrow time \ taken = \dfrac{22}{63}r^3[/tex]
