The contents of one 40 . lb bag of topsoil will cover 10....

The contents of one $40 .$ lb bag of topsoil will cover 10. square feet of ground to a depth of $1.0$ inch. What number of bags are needed to cover a plot that measures 200 . by $300 . \mathrm{m}$ to a depth of $4.0 \mathrm{~cm}$ ?

Key Concepts

Area Calculation

The technique of determining the size of a surface by multiplying two dimensions, such as length and width. This is essential in determining the extent over which a material, like topsoil, will be spread.

Volume Calculation

The process of computing the amount of space occupied within a three-dimensional region by multiplying area by depth or thickness. This concept is crucial when calculating the total quantity of material needed to cover a given area to a specific depth.

Unit Conversion

The process of translating measurements from one set of units to another to maintain consistency in calculations. This involves converting lengths, areas, or volumes from one system (e.g., metric) to another (e.g., imperial), ensuring that every measurement is in the correct unit for the final computation.

Dimensional Analysis

A method used to verify that equations and calculations are set up correctly by keeping track of units throughout the problem. This systematic approach ensures that all measured quantities cancel or combine appropriately to yield a result in the desired units.

Transcript

00:01 We know that one bag of soil covers a 10 foot by 10 foot by 1 inch area.

00:10 That's because it's 10 feet squared and 1 inch of depth.

00:19 And we want to know how many bags it'll take to cover this plot that is 200 meters by 300 meters by 4 centimeters for the depth.

00:30 In order to solve this problem, we can calculate the total volume of this plot and the total volume of this plot.

00:39 Divide this volume by this volume to see how many 40 pound bags it will take to fill this plot.

00:49 The important part of this though is that we have units that are the same.

00:54 So right now we're working with feet, inches, meters, and centimeters.

01:00 We're going to have to get all of those into one common unit.

01:05 You can use any common unit, but i'm going to use meters.

01:08 So first, here i have the conversion of feet to meters.

01:14 So i'm going to convert inches to feet and then these measurements of feet to meters.

01:26 Then i'll convert centimeters to meters and then we'll have a common unit of meters.

01:35 So first we know that there are 12 inches in one foot, so this 1 inch will become 1 12th of a foot, which is equal to 0 .0833 feet.

01:54 Now to convert these two measurements of feet to meters, we can multiply each of them by the conversion.

02:04 So 0 .3048 meters for every 1 foot for both of these measurements...

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