Heavy equipment operators excavate holes and load the material into dump trucks which take the soil away from the jobsite. The material removed from the hole increases in volume because air gets mixed in with it. This is called swell. Topsoil has a swell factor of $40 \%$. Calculate the total volume of topsoil excavated from the hole.
$108 m^3$
$378 m^3$
$270 m^3$
$162 m^3
Answer (2)
The total volume of topsoil excavated from the hole is calculated to be 151.2 m 3 . This is found by adding the initial volume of 108 m 3 to the increase in volume due to a swell factor of 40% . The correct answer is 151.2 m 3 .
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The initial volume of topsoil is 108 m 3 and the swell factor is 40% .
Calculate the increase in volume due to swell: 108 m 3 × 0.40 = 43.2 m 3 .
Determine the total volume by adding the initial volume and the increase in volume: 108 m 3 + 43.2 m 3 = 151.2 m 3 .
The total volume of topsoil excavated from the hole is 151.2 m 3 .
Explanation
Understanding the Problem We are given that the initial volume of topsoil excavated from the hole is 108 m 3 . The swell factor is 40% , which means the volume increases by 40% when the soil is excavated. We need to calculate the total volume of the topsoil after the swell.
Defining Variables and Swell Volume Let V 0 be the initial volume of the topsoil in the hole, so V 0 = 108 m 3 . Let S be the swell factor, so S = 40% = 0.40 . The increase in volume due to swell is V 0 × S = 108 × 0.40 .
Calculating Total Volume The total volume V T of the excavated topsoil is the initial volume plus the increase in volume: V T = V 0 + V 0 × S = V 0 ( 1 + S ) .
Substituting Values Substitute the given values: V T = 108 ( 1 + 0.40 ) = 108 ( 1.40 ) .
Calculating the Final Volume Calculate the total volume: V T = 108 × 1.40 = 151.2 m 3 .
Final Answer Therefore, the total volume of topsoil excavated from the hole is 151.2 m 3 .
Examples
Understanding swell factor is crucial in construction and earthmoving projects. For example, if you're planning to build a house with a basement, you need to excavate soil. Knowing the swell factor helps you estimate how much extra space you'll need to store the excavated soil temporarily, and how many dump truck loads will be required to haul it away. This ensures you have enough space and resources, preventing costly delays and mismanagement of materials. The swell factor impacts logistics, storage, and transportation planning in construction.
