Ryan is using a wheelbarrow that hols 3 cubic Ieat of soil. a) How many cubic yards will his wheelbarrow hold? b) If Ryan takes 32 loads wth his wheelbarrow how many cubic yards of soil will he move
The Correct Answer and Explanation is:
Of course. Here is the solution and explanation.
Correct Answer
a) The wheelbarrow holds 1/9 of a cubic yard, or approximately 0.11 cubic yards.
b) Ryan will move 3 and 5/9 cubic yards, or approximately 3.56 cubic yards of soil.
Explanation
This problem involves the conversion of units for volume, specifically from cubic feet to cubic yards, and then applying that conversion to a practical scenario.
Part a) How many cubic yards will his wheelbarrow hold?
To solve this, one must first understand the relationship between feet and yards. The fundamental relationship is:
1 yard = 3 feet
However, this is a linear measurement. The problem deals with volume, which is a three-dimensional measurement (length × width × height). Therefore, to find the conversion factor for cubic units, this linear factor must be cubed.
The volume of one cubic yard is:
1 yard × 1 yard × 1 yard
Substituting the value in feet:
3 feet × 3 feet × 3 feet = 27 cubic feet
This establishes the key conversion factor: 1 cubic yard = 27 cubic feet.
Ryan’s wheelbarrow holds 3 cubic feet. To find what fraction of a cubic yard this represents, divide the wheelbarrow’s volume by the total number of cubic feet in a cubic yard:
Volume in cubic yards = 3 cubic feet / 27 cubic feet = 1/9 cubic yards.
As a decimal, 1 ÷ 9 is 0.111…, which is commonly rounded to 0.11 cubic yards.
Part b) If Ryan takes 32 loads, how many cubic yards of soil will he move?
There are two primary methods to calculate the total volume.
Method 1: Calculate Total in Cubic Feet First
First, find the total volume of soil moved in cubic feet by multiplying the number of loads by the volume per load.
Total Volume (cubic feet) = 32 loads × 3 cubic feet/load = 96 cubic feet.
Next, convert this total volume from cubic feet to cubic yards using the conversion factor from Part a.
Total Volume (cubic yards) = 96 cubic feet / 27 cubic feet/yard = 3.555…
This can be expressed as the mixed fraction 3 and 5/9 cubic yards or rounded to 3.56 cubic yards.
Method 2: Use the Volume in Cubic Yards Per Load
From Part a, it was determined that one load is equal to 1/9 of a cubic yard. Multiply this by the number of loads.
Total Volume (cubic yards) = 32 loads × (1/9) cubic yards/load = 32/9 cubic yards.
Converting the improper fraction 32/9 to a mixed number gives 3 and 5/9 cubic yards.thumb_upthumb_down
