Question

Gold has a specific gravity of almost \(20 .\) A 5 -gallon bucket of water weighs 40 pounds. How much would a 5 -gallon bucket of gold weigh?

Short answer

A 5-gallon bucket of gold would weigh 800 pounds.

Step-by-step solution

Understand the Specific Gravity

The specific gravity of gold is given as 20. Specific gravity is the ratio of the density of a substance compared to the density of water. This means that gold is 20 times denser than water.

Determine the Weight of Water

A 5-gallon bucket of water weighs 40 pounds. Since the specific gravity is based on the density of water, we will use this information to calculate the weight of the same volume of gold.

Calculate the Weight of the Gold

The weight of the gold is found using the formula for specific gravity: \( \text{Weight of Gold} = \text{Specific Gravity} \times \text{Weight of Water} \). Therefore, \( \text{Weight of Gold} = 20 \times 40 = 800 \) pounds. This calculation shows that a 5-gallon bucket of gold weighs 800 pounds.

Key concepts

Understanding Specific Gravity

Specific gravity is a term used to describe the density of a material in relation to the density of water. When we say that gold has a specific gravity of 20, it means that gold is 20 times denser than water.

This concept is important because it helps us compare different substances based on their density. Density refers to how tightly packed the atoms are within a substance. For example, if you take the same volume of gold and water, gold would be much heavier than water due to its higher density.

• Specific gravity is a unitless number.
• It offers an easy way to compare the densities of different substances.
• A material with a specific gravity greater than 1 is denser than water.

Understanding this concept helps us solve the problem of determining how much a 5-gallon bucket of gold would weigh.

Comparing Densities: Gold versus Water

When discussing densities, we often compare a substance to water, because water has a well-known density of 1 gram per cubic centimeter. In this exercise, we're tasked with comparing gold, which has a much higher density than water.

In practical terms, this means that if you have two substances of equal volume, the one with the higher specific gravity (like gold in this case) will weigh more. Specifically, gold's specific gravity of 20 implies it's 20 times heavier than the same volume of water.

• Water serves as a common reference point for specific gravity values.
• The higher the specific gravity, the heavier the substance will be compared to water.

This understanding is crucial in fields like geology and materials science, where knowing the weight and density of materials can influence various practical applications.

Applying Mathematical Calculations

To determine the weight of a 5-gallon bucket of gold, we apply a straightforward mathematical calculation based on specific gravity. The specific gravity formula helps us calculate the weight of a substance given its volume and the density comparison to water.

The formula for specific gravity is: \[ \text{Weight of Substance} = \text{Specific Gravity} \times \text{Weight of the Same Volume of Water} \]

For this exercise, we know that a 5-gallon bucket of water weighs 40 pounds. Since gold has a specific gravity of 20, the calculation is performed as follows:

• Multiply: \( 20 \times 40 = 800 \) pounds
• A 5-gallon bucket of gold would weigh 800 pounds.

This calculation uses multiplication to scale the known weight of water to find the weight of gold, thereby making this mathematical step straightforward yet critically informative.