Grains of fine california beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.5 × 103 kg/m3. what mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 1.1 m on an edge?

0.30042 kg = 300.42 gram

Explanation:

Given data:

Density, D = 2.5 × 10³ kg/m³

Radius, r = 50 μm = 50 × 10⁻⁶ m³

edge of the cube, a = 1.1 m

Now, Mass (M) is given as :

M = Density × Volume

M =

or

M =

or

M = 1.30 × 10⁻⁹ Kg

Thus, the mass of single sand grain is 1.30 × 10⁻⁹ Kg

Now, the number of grains required for the 1.1 m edge cube total surface area

the surface area of the cube = number of sand grains (n) × (surface area of the single sand grain)

6 × a² = n × 4πr²

on substituting the values

we have

6 × 1.1² = n × 4 × π × (50 × 10⁻⁶)²

n = 231.092 × 10⁶

Thus, the mass of the sand required will be = n × M = 231.092 × 10⁶ × 1.30 × 10⁻⁹ Kg = 0.30042 kg = 300.42 gram

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answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.