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2 December, 00:55

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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  1. 2 December, 03:29
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    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.
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