Question

A pile of earth removed from an excavation is a cone measuring 6ft high and 30ft across its base. How many trips will it take to haul away the earth using a dump truck with a capacity of 125 cubic feet?

Answer 1

Answer: 14

Step-by-step explanation:

Given

Excavation cone measures

height $h=6\ ft$

Diameter $d=30\ ft$

Truck can dump $125\ ft^3$ at a time

The volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

Putting values

$\Rightarrow V=\dfrac{1}{3}\times \pi\times 15^2\times 6\\\Rightarrow V=1413.9\approx 1414\ ft^3$

No of trips(N) required to accumulate this much volume is given by

$\Rightarrow N=\dfrac{1414}{125}=13.3\approx 14$

Therefore, 14 trips are necessary to accumulate a cone of volume $1414\ ft^3$