Question

A vessel in the form of a hemispherical bowl is full of water. The contents are emptired into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

Answer 1

The radius of the hemispherical bowl is 6 cm.

The volume of the bowl = 2/3πr³

Volume of bowl = 2/3 × 3.14 × 6 × 6 × 6

= 6.28 × 2 × 6 × 6

= 452.16 cm³

The radius of cylinder is 4 cm.

Volume of cylinder = πr²h

Volume of bowl = Volume of cylinder

452.16 = 3.14 × 4 × 4 × h

452.16/12.56 = h

h = 36 cm.

Therefore the height of water in cylinder is 36 cm.

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Answer 2

Answer:

The height of water in cylindrical container is 9 cm .

Step-by-step explanation:

Given as :

A vessel in the form of a hemispherical bowl is full of water.

The contents are emptied into a cylinder.

The radius of hemispherical bowl = R = 6 cm

The radius of cylindrical container = r = 4 cm

Let The height of cylindrical container = h cm

And Height of water in cylindrical container = height of cylinder = h cm

Since The water from hemispherical bowl is emptied into a cylinder.

So, The volume of bowl = volume of container

Now, According to question

∵ Volume of hemispherical bowl = $v_1$ = $\dfrac{2}{3}$ $\pi$ radius³

Or,  $v_1$ = $\dfrac{2}{3}$ × $\pi$ × R³

Or, $v_1$ = $\dfrac{2}{3}$ × 3.14 × 6³

∴   $v_1$ =  452.16 cubic cm             ........1

And

Volume of cylindrical container  = $v_2$ =  $\pi$ radius² height

Or,  $v_2$ = $\pi$ × r² × h

Or, $v_2$ =  3.14 × 4² × h

∴    $v_2$ =  50.24 × h cubic cm              ........2

Again

volume of bowl = volume of container

i.e  $v_1$  = $v_2$

or, 452.16 cubic cm   =  50.24 × h

∴   h = $\dfrac{452.16}{50.24}$

i.e height = h = 9 cm

Hence, The height of water in cylindrical container is 9 cm . Answer