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22 April, 06:08

A swimming pool measures 50.0 meters by 25.0 meters. How many grams of water are needed to fill the pool, whose average depth is 7.6 feet? Assume the density of water to be 1.0 g/mL. Use significant figures. Use "E" for scientific notation. Do not enter "grams" as part of your answer.

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  1. 22 April, 06:26
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    This question requires us to find the volume of the swimming pool. We will assume that the shape of the pool is rectangular with a constant depth throughout, resulting in a rectangular prism overall. The volume of a rectangular prism is simply the product of the length, width and depth of the pool.

    V = l·w·d

    We are told the length is 50 m and the width is 25 m. However, we are told the depth is 7.6 ft. Therefore, we must convert these units to m in order to find the volume properly.

    7.6 ft x 0.3048 m/ft = 2.316 m

    V = (50 m) (25 m) (2.316 m)

    V = 2895.6 m³

    The density of the pool is 1g/mL. We need to convert mL to m³ in order to use the volume we calculated.

    1 mL = 1 cm³

    1000000 cm³ = 1 m³

    1 g/mL x 1 mL/1 cm³ = 1 g/cm³

    1 g/cm³ x 1000000 cm³/m³ = 1000000 g/m³

    1000000 g/m³ x 2895.6 m³ = 2.9 x 10⁹ = 2.9E9 g

    There are 2.9E9 grams of water in the pool.
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