Question

A metallic cylinder of radius 2.1m & height 10m has mass of 396kg. Determine whether it'll float or sink in water.​

Answer 1

Given : A metallic cylinder of radius 2.1 m & height 10 m has mass of 396kg.

To Find: whether it'll float or sink in water.​

Solution:

radius  r = 2.1 m

Height = 10 m

Volume of cylinder = πr²h

= (22/7) * (2.1)² * 10

=  22 * 2.1 * 0.3 * 10

=  66 * 2.1  m³

mass = 396 kg

Density = mass / Volume

=> Density =  396 / 66 * 2.1

=> Density = 6/2.1

=> Density =  2.857 kg/m³

Density of water 997 kg/m³

As Density is less than water so it will float

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Answer 2

$given \: radius = 2.1, height \: = 10m \: and \: mass = 396kg$

$now, volume \: of \: cylindr = r {}^{2} h$

$volume = \frac{22}{7} \times 2.1 \times 2.1 \times 10 = 138.6 {m}^{2}$

$now, density = \frac{mass}{volume} = \frac{396}{138.6} = 2.86kg / {m}^{3}$

$now, we \: know \: that, density \: of \: water \: is \: 1000kg / {m}^{3}$

$now, density \: of \: cylinder \: < \: density \: of \: water$

hence the cylinder float on the surface of the water