Question

A spherical tank with a radius of 0.25 m is filled with water (ρ = 1000 kg/m3). Calculate the mass and weight of the water in SI units.

Answer 1

The mass of the water is 65.5 kg. The weight of the water is 641.9 kgm/s²

What is the mass of a spherical tank?

The mass of a spherical tank is the space contained in the tank. The mass of the spherical tank can be determined by first finding the volume of the tank, then using the relation of density, mass, and volume to find the mass.

From the given parameter:

• The radius of the tank = 0.25 m
• The density of the water = 1000 kg/m³

The volume of the tank can be determined by using the formula:

$\mathbf{V = \dfrac{4}{3}\pi r^3}$

$\mathbf{V = \dfrac{4}{3}\pi (0.25)^3}$

V = 0.0655 m³

Using the relation that:

$\mathbf{Density = \dfrac{mass}{volume}}$

$\mathbf{1000 \ kg/m^3= \dfrac{mass}{0.0655 \ m^3}}$

mass = 1000 kg/m³ × 0.0655 m³

mass = 65.5 kg

The weight of the water can be determined by using the formula:

Weight = mass × gravity (i.e. acceleration due to gravity)

Weight = 65.5 kg × 9.8 m/s²

Weight = 641.9 kgm/s²

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Answer 2

The mass of the water in spherical tank is 65.4kg.

The weight of the water in spherical tank is 640.8 Newtons.

Given the data in the question:

• Radius of the spherical tank; $r = 0.25m$

• Density of water; $p = 1000kg/m^3$

Mass of water; $m_w = \ ?$

Weight of water; $Ww = \ ?$

Density

Density $p$ is simply the measure of the compactness of the mass of a substance. It is expressed as;

$Density = \frac{Mass}{Volume}$

To determine the mass and weight of the water in spherical tank,

we calculate the Volume of the spherical tank.

$V = \frac{4}{3}\pi r^3$

We substitute in our given values

$V = \frac{4}{3} * \pi * (0.25m)^3\\ \\V = \frac{4}{3} * \pi * 0.015625m^3\\\\V = 0.0654 m^3$

Now, we calculate the mass of the water; using the expression above.

$Density = \frac{Mass}{Volume}\\Mass = Density * Volume$

We substitute in our values

$Mass = 1000kg/m^3 \ *\ 0.0654m^3\\\\Mass = 65.4kg$

Hence, the mass of the water in spherical tank is 65.4kg.

Next we calculate the Weight which is expressed as;

$Weight = mass\ *\ Acceleration\ of\ gravity$

Where acceleration of gravity $g = 9.8m/s^2$

We substitute in our values

$Weight = 65.4kg * 9.8m/s^2\\\\Weight = 640.8kgm/s^2\\\\Weight = 640.8N$

Therefore, the weight of the water in spherical tank is 640.8 Newtons.

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