Question

A cuboidal container of dimension 10 cm by 8cm and by 6cm filled with water and this water is poured into a cylindrical container of radius 7 cm . find the height of water in cylinder​.



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Answer 1

Answer is 3.1

Full answer is photo below.

I hope this answer is you useful.

Answer 2

★ Concept :-

Here the concept of Volume of Cylinder and Volume of Cuboid has been used. We are given that the cuboidal container contains water. Since we are give it's full dimensions, then easily we can find the volume of container. Since water occupies the space of container in which it is kept, then the volume of water will be same as that of container. Now this same water is transferred into a cylindrical container. So the volume of water will remain equal in that too. Then we will have an equation where we need to find the height of water in cylindrical container and from which we can find the values.

Let's do it !!

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★ Formulas Used :-

$\;\;\boxed{\sf{\pink{Volume\;of\;Cuboid\;=\;Length\:\times\:Breadth\:\times\:Height}}}$

$\;\;\boxed{\sf{\pink{Volume\;of\;Cylinder\;=\;\pi\:\times\:r^{2}\:\times\:h}}}$

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★ Solution :-

Given,

» Length of Cuboidal container = L = 10 cm

» Breadth of Cuboidal container = B = 8 cm

» Height of Cuboidal container = H = 6 cm

» Radius of the Cylindrical container = r = 7 cm

• Let the height of the Cylindrical Container be h cm .

• For the volume of water ::

We know that,

>> Volume of Cuboidal container = Volume of water in Cuboidal container

(Since container is filled)

Let's now find the Volume of Container.

This is given as,

$\;\;\tt{\rightarrow\;\;Volume\;of\;Cuboid\;=\;Length\:\times\:Breadth\:\times\:Height}$

By applying values, we get

$\;\;\tt{\rightarrow\;\;Volume\;of\;Cuboid\;=\;L\:\times\:B\:\times\:H}$

$\;\;\tt{\rightarrow\;\;Volume\;of\;Cuboid\;=\;10\:\times\:8\:\times\:6}$

$\;\;\tt{\rightarrow\;\;Volume\;of\;Cuboidal\;=\;10\:\times\:48}$

$\;\;\bf{\rightarrow\;\;Volume\;of\;Cuboidal\:Container\;=\;480\;\:cm^{3}}$

This gives us the volume of water in Cuboidal container as 480 cm³.

• For the Height of water in Cylindrical container ::

Since the volume of water will remain same.

So, we can equate it easily in the formula .

$\;\;\tt{\Longrightarrow\;\;Volume\;of\;Cylinder\;=\;\pi\:\times\:r^{2}\:\times\:h}$

Since water takes the shape of cylinder. This means that we can apply values in this formula.

$\;\;\tt{\Longrightarrow\;\;\pi\:\times\:r^{2}\:\times\:h\;=\;Volume\;of\;Water}$

By applying values, we get

$\;\;\tt{\Longrightarrow\;\;\dfrac{22}{7}\:\times\:(7)^{2}\:\times\:h\;=\;480}$

$\;\;\tt{\Longrightarrow\;\;\dfrac{22}{7}\:\times\:49\:\times\:h\;=\;480}$

By cancelling 49 with 7, we get

$\;\;\tt{\Longrightarrow\;\;22\:\times\:7\:\times\:h\;=\;480}$

$\;\;\tt{\Longrightarrow\;\;154\:\times\:h\;=\;480}$

$\;\;\tt{\Longrightarrow\;\;h\;=\;\dfrac{480}{154}}$

$\;\;\tt{\Longrightarrow\;\;h\;=\;3.12\;\:cm}$

Here we have rounded off the answer to two decimal points.

This is the required answer.

$\;\underline{\boxed{\tt{Height\;of\;water\;in\;Cylinder\;=\;\bf{\purple{3.12\;\:cm^{2}}}}}}$

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★ More to know :-

$\;\sf{\leadsto\;\:L.S.A.\;of\;Cuboid\;=\;2(L\:+\:B)\:times\:H}$

$\;\sf{\leadsto\;\:T.S.A.\;of\;Cuboid\;=\;2(LB\:+\:BH\:+\:LH)}$

$\;\sf{\leadsto\;\:Diagonal\;of\;Cuboid\;=\;\sqrt{(L^{2}\:+\:B^{2}\:+\:H^{2})}}$

$\;\sf{\leadsto\;\;C.S.A.\;of\;Cylinder\;=\;2\pi rh}$

$\;\sf{\leadsto\;\;T.S.A.\;of\;Cylinder\;=\;2\pi rh\:+\;2\pi r^{2}}$

• L = Length of Cuboid

• B = Breadth of Cuboid

• H = Height of Cuboid

• r = Radius of Cylinder

• h = Height of Cylinder