Respuesta :
Answer:
mass of water = 2962656000 = 2.963 E9 grams
Explanation:
1 ft = 0.3048 m
Therefore:
7.2 ft = 2.19456 m
First, we will get the volume of the swimming pool as follows:
The swimming pool has a rectangular shape, this means that:
volume of pool = length * width * depth
volume of pool = 45 * 30 * 2.19456 = 2962.656 m^3
Now, we will get the mass of needed water as follows:
density = mass / volume
we have:
density = 1 g/ml
volume = 2962.656 m^3 = 2962656000 ml
Substitute to get the mass of water as follows:
mass of water = density * volume = 1 * 2962656000
mass of water = 2962656000 = 2.963 * 10^9 grams
Hope this helps :)
mass of water = 2962656000 = 2.963 E9 grams
Explanation:
1 ft = 0.3048 m
Therefore:
7.2 ft = 2.19456 m
First, we will get the volume of the swimming pool as follows:
The swimming pool has a rectangular shape, this means that:
volume of pool = length * width * depth
volume of pool = 45 * 30 * 2.19456 = 2962.656 m^3
Now, we will get the mass of needed water as follows:
density = mass / volume
we have:
density = 1 g/ml
volume = 2962.656 m^3 = 2962656000 ml
Substitute to get the mass of water as follows:
mass of water = density * volume = 1 * 2962656000
mass of water = 2962656000 = 2.963 * 10^9 grams
Hope this helps :)
The mass of water to fill the swimming pool of length 45 m, width 30 m and a depth of 72 ft is [tex]\boxed{2.963{\text{E}}9}[/tex]
Further explanation:
Density is considered as a characteristic property of the substance. It is defined as the mass per unit volume. It is generally represented by [tex]\rho[/tex].
The formula to calculate the density of water is,
[tex]{\text{Density of water}}\left( {\rho\right){\text{ = }}\frac{{{\text{Mass of water}}\left({\text{M}}\right)}}{{{\text{Volume of water}}\left({\text{V}}\right)}}[/tex] …… (1)
The swimming pool is in the shape of a cuboid. Its length, width, and depth are 45 m, 30 m and 7.2 ft.
Firstly, we have to convert the depth of the pool from feet to meters. The conversion factor for this is,
[tex]{\text{1 ft}}={\text{0}}{\text{.3048m}}[/tex]
So the depth of the pool is calculated as follows:
[tex]\begin{gathered}{\text{Depth of pool}}=\left({7.2\;{\text{ft}}}\right)\left({\frac{{{\text{0}}{\text{.3048m}}}}{{{\text{1 ft}}}}}\right)\\={\text{2}}{\text{.19456m}}\\\end{gathered}[/tex]
The formula to calculate the volume of the pool is as follows:
[tex]{\text{Volume of pool}}=\left({{\text{length of pool}}}\right)\left({{\text{width of pool}}} \right)\left( {{\text{depth of pool}}}\right)[/tex] …… (2)
The length of the pool is 45 m.
The width of the pool is 30 m.
The depth of the pool is 2.19456 m.
Substitute these values in equation (2).
[tex]\begin{gathered}{\text{Volume of pool}}=\left({{\text{45m}}}\right)\left({{\text{30m}}}\right)\left({{\text{2}}{\text{.19456m}}}\right)\\=2962.656\;{{\text{m}}^{\text{3}}}\\\end{gathered}[/tex]
As the pool is filled with water so the volume of water is the same as that of the swimming pool and therefore the volume of water is [tex]2962.656\;{{\text{m}}^{\text{3}}}[/tex].
Rearrange equation (1) to calculate the mass of water.
[tex]{\text{Mass of water}}=\left({{\text{Density of water}}}\right)\left({{\text{Volume of water}}}\right)[/tex] ……. (3)
The conversion factor to convert the volume of water in mL is as follows:
[tex]1\;{{\text{m}}^{\text{3}}}={10^6}\;{\text{mL}}[/tex]
So the volume of water is calculated as follows:
[tex]\begin{gathered}{\text{Volume of water}}=\left({2962.656\;{{\text{m}}^{\text{3}}}}\right)\left({\frac{{{{10}^6}\;{\text{mL}}}}{{1\;{{\text{m}}^3}}}}\right)\\=2962656000\;{\text{mL}}\\\end{gathered}[/tex]
The density of water is 1 g/mL.
The volume of water is [tex]2962656000\;{\text{mL}}[/tex].
Substitute these values in equation (3).
[tex]\begin{gathered}{\text{Mass of water}}=\left({\frac{{{\text{1 g}}}}{{{\text{1 mL}}}}}\right)\left({{\text{2962656000 mL}}}\right)\\={\text{2962656000g}}\\\end{gathered}[/tex]
So [tex]{\text{2962656000 g}}[/tex] water is needed to fill the swimming pool. Its value up to 3 significant figures is [tex]2.963\times{10^9}[/tex] and it is written as [tex]2.963{\text{E}}9[/tex] in scientific notation.
Learn more:
1. Calculation of volume of gas: https://brainly.com/question/3636135
2. Determine how many moles of water produce: https://brainly.com/question/1405182
Answer details:
Grade: Middle School
Subject: Chemistry
Chapter: Density
Keywords: density, mass, volume, swimming pool, length, width, depth, water, volume of water, density of water, significant figures, scientific notation, 2.963E9, 2962656000 g.
