Question

="TexFormula1" title="\color {white}\boxed{\colorbox{black} { QUESTION♡}} " alt="\color {white}\boxed{\colorbox{black} { QUESTION♡}} " align="absmiddle" class="latex-formula">
​ ​ A hemispherical bowl of internal diameter 30 cm contains liquid liquid is to be filled into a cylindrical shape bottles each of diameter 5 cm and height 6 cm find the number of bottles necessary to empty. the bowl ??
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✦diagram if necessary
plss help !!​

Answer 1

$\\ \qquad{\rule{200pt}{3pt}}$

❖ Information provided with us ❖

• ➪ Internal diameter of hemispherical bowl

$\longrightarrow \rm30 \: cm$

• ➪ Internal radius of hemispherical bowl

$\longrightarrow \rm \: radius = \dfrac{diameter}{2} = \dfrac{30}{2} = 15 \: cm$

➪ Height of cylindrical bottle

$\longrightarrow \rm \: h = 6 \: cm$

➪ Diameter of cylindrical bottle

$\longrightarrow \rm \: 5 \: cm$

➪ Radius of cylindrical bottle

$\longrightarrow \rm \: radius = \dfrac{diameter}{2} = \dfrac{5}{2} = 2.5\: cm$

❖ What we have to find ❖

➪ The required number of bottles necessary to empty the bowl.

✞︎ Solution ✞︎

❒ Concept used ❒

➪ In order to number of bottles necessary to empty the bowl take ,

$\clubsuit$ Volume of water in bowl =

$\implies \rm \: Numbers \: of \: bottles \times Volume \: of \: water \: in \: one \: bottle$

❒ Assumption ❒

• ➪ Consider the number of bottles be $\bf{n}$

❒ So ❒

➪ By substituting the given values in above formula

$\rm : : \implies \: \bigg ( \dfrac{2}{3} \bigg)\pi \: {r}^{3} = n \times \pi \: {r}^{2} h$

$\rm : : \implies \: \bigg ( \dfrac{2}{3} \bigg) \cancel{\pi }\: {r}^{3} = n \times \cancel{\pi }\: {r}^{2} h$

$\rm : : \implies \: \bigg ( \dfrac{2}{3} \bigg) \times {(15)}^{3}= n \times \: {(2.5)}^{2} \times 6$

$\rm : : \implies \: \bigg ( \dfrac{2}{3} \bigg) \times 3375= n \times \: 6.25 \times 6$

$\rm : : \implies \: \bigg ( \dfrac{3375 \times 2}{3} \bigg) = n \times 37.5$

$\rm : : \implies \: \bigg ( \dfrac{675 0}{3} \bigg) = n \times 37.5$

$\rm : : \implies \: 2250 = 37.5 \: n$

$\rm : : \implies \: \: n = \dfrac{2250}{37.5}$

$\rm : : \implies \boxed{\bf n = 60}$

❒ Therefore ❒

➪ The required number of bottles necessary to empty the bowl is

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:\:60\:}}}}$

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Answer 2

60 bottles required.

calculate the volume of both shapes

For hemispherical bowl:

$\sf volume: \dfrac{2}{3} \pi r^3$                         [diameter: 30 cm, radius: 15 cm]

$\rightarrow \sf volume: \dfrac{2}{3} \pi (15)^3$

$\rightarrow \sf volume: 2250\pi \ cm^3$

For each cylindrical bottles:

$\sf volume: \pi r^2h$                          ["r" is 2.5 cm, "h" is 6 cm]

$\rightarrow \sf volume: \pi (2.5)^2(6)$

$\rightarrow \sf volume: 37.5 \pi \ cm^3$

So number of required bottles:

• volume of hemisphere/volume of each cylindrical bottle

• 2250π/37.5π

• 60 bottles