Some important concept before solving answer :-
[tex] \\ [/tex]
When ever there is three dimensional figure remember, where one figure is related to other then there's always relation with volume.
So it may get pretty difficult to understand therefore I am dividing into small parts for better understanding.
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[tex] \pmb{ \bf \dag\cal{Part \ One:}}[/tex]
As we know there will be relation of volume, so let's find volume of the cone first.
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Given :-
⭑Height = 10 cm
⭑radius = 3cm
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To find :
⭑volume of cone
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Let represent :-
⭑Height as : h
⭑radius as : r
⭑volume of cone as : v
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Formula to find volume of cone :-
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[tex] \bigstar\boxed{ \rm v = \pi {r}^{2} \times \frac{h}{3} }[/tex]
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So let's find v!
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[tex] \dashrightarrow\sf v = \pi {r}^{2} \times \dfrac{h}{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22}{7} \times {3}^{2} \times \dfrac{10}{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22}{7} \times {3} \times 3\times \dfrac{10}{3} [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22}{7} \times {\cancel3} \times 3\times \dfrac{10}{\cancel3} [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times \dfrac{10}{1} [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22}{7}\times 3\times10[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22\times 3\times10}{7}[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{22\times 30}{7}[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf v = \dfrac{660}{7}[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\bf v =94.3 {cm}^{3} [/tex]
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[tex] \pmb{ \bf \dag\cal{Part \: \: Two:}}[/tex]
So remember that cone filled with water is equal to volume of cone.
volume of water filled in cone = volume of water in cuboid.
So you probably thinking that above sentence is wrong , cause they haven't told volumes of cuboid and cone are equal, but we have to find depth of water filled not depth of cuboid.
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Given :-
⭑Volume of cuboid = 94.3 cm³
⭑Length of cuboid = 5cm
⭑Width of cuboid = 3cm
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To find :-
⭑Depth of water in cuboid
[tex] \\ [/tex]
Let represent:-
⭑Volume of cuboid as : V'
⭑Length of cuboid as : L
⭑Width of cuboid as : W
⭑Depth of water in cuboid as : D
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Formula to find volume of cuboid :-
[tex] \\ \\ [/tex]
[tex] \bigstar\boxed{ \rm V'= W \times L \times D }[/tex]
By using this formula we can find depth of cuboid.
[tex] \\ \\ [/tex]
[tex] : \implies \sf V'= W \times L \times D [/tex]
[tex] \\ \\ [/tex]
[tex] : \implies \sf 94.3= D \times 3 \times 5[/tex]
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[tex] : \implies \sf \dfrac{943}{10\times 3 \times 5} = D [/tex]
[tex] \\ \\ [/tex]
[tex] : \implies \sf \dfrac{943}{10 \times 15} = D [/tex]
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[tex] : \implies \sf \dfrac{943}{150} = D [/tex]
[tex] \\ \\ [/tex]
[tex] : \implies \sf D = \dfrac{943}{150} [/tex]
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[tex] : \implies \bf D = 6.3cm[/tex]
[tex] \\ \\ [/tex]
Required Answer:-
Depth = 6.3 cm
