Calculate the depth to which Avogadro's number of table...

Calculate the depth to which Avogadro's number of table tennis balls would cover Earth. Each ball has a diameter of $3.75 \mathrm{cm} .$ Assume the space between balls adds an extra
25.0\% to their volume and assume they are not crushed by their own weight.

Key Concepts

Avogadro's Number

Avogadro's number, approximately 6.022×10^23, is the number of entities (such as atoms, molecules, or in this case, table tennis balls) in one mole. It is a fundamental constant in chemistry and physics that bridges the microscopic and macroscopic worlds, allowing scientists to count individual particles by weighing macroscopic amounts.

Volume of a Sphere

The volume of a sphere is a fundamental geometric concept calculated by the formula (4/3)?r^3, where r is the radius. This concept is essential when determining how much space a spherical object occupies, which is necessary to calculate the total volume taken up by multiple spherical objects.

Effective Volume Increase Due to Packing

When objects such as spheres are packed, there is typically extra space between them. In this problem, an extra 25% volume is added to account for the gaps between the table tennis balls. This adjustment is a practical application of packing efficiency, which is important in many fields including material science and logistics.

Earth's Surface Area Calculation

Calculating Earth's surface area is vital when spreading a given volume over the planet. The surface area formula for a sphere is 4?R^2, where R is Earth's radius. This step is key in finding how deep a layer would be if a given volume of material is distributed evenly over Earth's curved surface.

Volume to Depth Conversion

The process of converting a total volume spread over an area into a depth involves dividing the volume by the area. This calculation transforms the three-dimensional volume information into a one-dimensional depth measurement, allowing for an understanding of how thick a layer of material would be if applied uniformly.

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