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GCSE Mathematics shape question Watch

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    Hello,
    I am stuck on this gcse question because i haven't really come across depth before and don't actually know how to get the answer.
    Any help is appreciated.
    Thanks.
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    (Original post by Blaze3211)
    Hello,
    I am stuck on this gcse question because i haven't really come across depth before and don't actually know how to get the answer.
    Any help is appreciated.
    Thanks.
    You've worked out the volume of the whole container, but you don't need to do this.

    First you need to find the volume of the water before putting the sphere into it as follows:

    Old water volume = 12 \times 11 \times 8 = 1056cm^3

    Then find the volume of the sphere

    Volume of sphere  = \frac{4}{3} \times \pi \times r^3

     = \frac{4}{3} \times \pi \times 3.5^3

     = \frac{4}{3} \times \pi \times 42.875

     = 179.59438cm^3

    Then find the new volume of water by adding the volume of the sphere to the old volume of water

    New water volume  = 1056cm^3 + 179.59438cm^3 = 1235.59438cm^3

    Then find the depth of the new water

    New water depth = 1235.59438 = length \times width \times depth

     1235.59438 = 12 \times 11 \times depth

     1235.59438 = 132 \times depth

     \frac{1235.59438}{132} = depth

     depth = 9.360563485

    Then finally minus the original depth of water (8)

     9.360563485 - 8 = 1.36cm (3s.f.)

    So the water rose 1.36cm
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    (Original post by Ryan14)
    You've worked out the volume of the whole container, but you don't need to do this.

    First you need to find the volume of the water before putting the sphere into it as follows:

    Old water volume = 12 \times 11 \times 8 = 1056cm^3

    Then find the volume of the sphere

    Volume of sphere  = \frac{4}{3} \times \pi \times r^3

     = \frac{4}{3} \times \pi \times 3.5^3

     = \frac{4}{3} \times \pi \times 42.875

     = 179.59438cm^3

    Then find the new volume of water by adding the volume of the sphere to the old volume of water

    New water volume  = 1056cm^3 + 179.59438cm^3 = 1235.59438cm^3

    Then find the depth of the new water

    New water depth = 1235.59438 = length \times width \times depth

     1235.59438 = 12 \times 11 \times depth

     1235.59438 = 132 \times depth

     \frac{1235.59438}{132} = depth

     depth = 9.360563485

    Then finally minus the original depth of water (8)

     9.360563485 - 8 = 1.36cm (3s.f.)

    So the water rose 1.36cm
    Thanks a lot i understand this now.
 
 
 
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