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Math Help - volume of elliptical object

  1. #1
    mat
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    Post volume of elliptical object

    hello I have to find the volume in metres cubed and in litres cubed of an above ground swimming pool. the surface area of the pool is of an axis 2 metres and 3 metres.the depth is 1.3 metres. so 2 times 3 times 1.3m=7.8 metres cubed. how to find how many litres correct to the nearest 10 litres? I need answer in about 24 hours thanks.
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    Quote Originally Posted by mat View Post
    hello I have to find the volume in metres cubed and in litres cubed of an above ground swimming pool. the surface area of the pool is of an axis 2 metres and 3 metres.the depth is 1.3 metres. so 2 times 3 times 1.3m=7.8 metres cubed. how to find how many litres correct to the nearest 10 litres? I need answer in about 24 hours thanks.
    According to your headline and the wording of the question I assume that the base area of the pool has to be an ellipse.

    1. Area of an ellipse:

    A_{elli} = \pi \cdot a \cdot b ...... Sub in the values for a and b (in meters!)

    A_{elli}=\pi \cdot 2 \cdot 3 = 6\pi\ m^2 ...... therefore the volume of the pool is:

    V_{pool}=A_{elli} \cdot 1.3\ m = 7.8\pi\ m^3\approx24.5044227\ m^3

    Use the property: One liter is the same as one decimeter cubed and one decimeter is the same as 10 cm. Therefore: 1m^3 = 1,000\ l

    So the pool contains:

    V_{pool}=24.5044227\ m^3 \cdot 1,000\frac{l}{m^3}= 24504.4227\ dm^3 \approx 24500\ l to the nearest 10 l.
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