Question

Answer the Question the volume based Question. I will make uh brainliest + 50 points​

Answer 1

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

$\sf volume \ of \ cone = \dfrac{1}{3} \pi r^2 h$

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$\rightarrow \sf \dfrac{1}{3} * \dfrac{22}{7} * r^2 * 14 = 132$

simplify

$\rightarrow \sf \dfrac{44}{3} * r^2= 132$

change sides

$\rightarrow \sf r^2= \dfrac{132(3)}{44} = 9$

square root both sides

$\rightarrow \sf r = 3$

∴ Hence the radius of cone (Shape B is 3 cm)

To show the time taken

volume = unit rate × time taken

$\sf volume \ of \ hemi -sphere = \dfrac{2}{3} \pi r^3$

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$\sf \rightarrow \dfrac{2}{3} \pi r^3 = 6 * time \ taken$

Insert values

$\sf \rightarrow \dfrac{2}{3} *\dfrac{22}{7} \ r^3 = 6 * time \ taken$

exchange sides

$\sf \rightarrow time \ taken = \dfrac{2}{3} *\dfrac{22}{7} \ r^3 *\dfrac{1}{6}$

simplify following

$\sf \rightarrow time \ taken = \dfrac{22}{63}r^3$