Question

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

Answer 1

The radius of bowl is 3.5 cm.

Volume of bowl is 2/3πr³

= 2/3 × 22/7 × 3.5 × 3.5 × 3.5

= 2/3 × 22 × 0.5 × 3.5 × 3.5

= 89.83 cm³

Radius of cylinder is 7 cm

Volume of cylinder = Volume of bowl

89.83 = πr²h

89.83 = 22/7 × 7 × 7 × h

89.83 / 154 = h

h = 0.583 cm

Approx . h = 0.6 cm

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Answer 2

The height of water rise in cylinder is 0.58 cm .

Step-by-step explanation:

Given as :

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

The internal radius of bowl = r = 3.5 cm

According to question

Volume of water in bowl = volume of hemispherical bowl = V = $\dfrac{2}{3}$ π r³

where r is radius

Or,  V = $\dfrac{2}{3}$ × 3.14 × (3.5 cm)³

Or, V = $\dfrac{2}{3}$ × 3.14 × 42.84 cm³

∴    V = 89.67 cubic cm

So, volume of hemispherical bowl = V = 89.67 cubic cm

Again

The water are emptied in a right circular cylinder

The radius of cylinder = r' = 7 cm

The height of cylinder = h cm

Now,

Volume of cylinder = V' = π r² h

Or, V' =  3.14 × (7 cm)²  × h cm

Or, V' = 3.14  × 49 cm²  × h cm

∴   V' = 153.86 h cubic cm

volume of cylinder = 153.86 ×  h

As water if poured from bowl and cylinder

Volume of bowl = volume of cylinder

i.e  V = V'

Or,  89.67 cubic cm = 153.86 h cubic cm

Or,  h = $\dfrac{89.67}{153.86}$

∴     h = 0.58 cm

So, The height of water rise in cylinder = h = 0.58 cm

Hence, The height of water rise in cylinder is 0.58 cm . Answer