A dump truck driver is delivering loads of sand for making sandbags to protect homes from flooding. Each load contains 12 m3 of sand and piles up into the shape of a cone as shown below. It is estimated that the pile will be large enough when it is 17m across and 9m high. How many truck loads of sand are needed?

Question

Erik Byrd

Mathematics

19 January, 04:06

A dump truck driver is delivering loads of sand for making sandbags to protect homes from flooding. Each load contains 12 m3 of sand and piles up into the shape of a cone as shown below. It is estimated that the pile will be large enough when it is 17m across and 9m high. How many truck loads of sand are needed?

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Answers (1)

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Gunner Chang · Answer 1

57

Step-by-step explanation:

The volume of a cone is given by the formula ...

V = (1/3) πr²h

For a pile with a radius of 8.5 m and a height of 9 m, the volume is ...

V = (1/3) π (8.5 m) ² (9 m) = 216.75π m³ ≈ 680.94 m³

Then the number of truckloads required to create that size pile will be ...

(680.94 m³) / (12 m³/truck) = 56.745 trucks

Even a partial truck load entails another trip, so ...

57 truck loads of sand are needed.