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

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=(1)/(3)\pi r^2h`

Putting values

`\Rightarrow V=(1)/(3)* \pi* 15^2* 6\\\Rightarrow V=1413.9\approx 1414\ ft^3`

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

`\Rightarrow N=(1414)/(125)=13.3\approx 14`

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