Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 85

Chapter 1, Problem 85

A 40-lb container of peat moss measures 14 * 20 * 30 in. A 40-lb container of topsoil has a volume of 1.9 gal. (b) How many bags of peat moss are needed to cover an area measuring 15.0 ft * 20.0 ft to a depth of 3.0 in.?

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Convert the dimensions of the peat moss container from inches to feet to find its volume in cubic feet. Use the conversion factor: 1 ft = 12 in.

Calculate the volume of the peat moss container in cubic feet using the formula: Volume = length \times width \times height.

Determine the volume of peat moss needed to cover the area by calculating the total volume required: Area \times depth. Convert the depth from inches to feet before calculating.

Divide the total volume of peat moss needed by the volume of one container of peat moss to find the number of containers required.

Round up to the nearest whole number, as you cannot have a fraction of a container.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Volume Calculation

To determine how many bags of peat moss are needed, it's essential to calculate the volume of the area to be covered. The volume can be found using the formula: Volume = Area × Depth. In this case, the area is 15.0 ft × 20.0 ft, and the depth is converted from inches to feet for consistency.

Unit Conversion

Unit conversion is crucial in this problem as it involves different units of measurement. The volume of the topsoil is given in gallons, while the area and depth are in feet. Understanding how to convert between cubic feet and gallons will allow for accurate comparisons and calculations of the materials needed.

Density and Weight Relationships

The relationship between weight and volume is important for determining how many bags of peat moss are required. Knowing the weight of the peat moss (40 lbs) and its volume (calculated from its dimensions) allows for the determination of how many bags are necessary to achieve the desired coverage. This concept ties together the physical properties of the materials involved.

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