The volume of all the oceans is [tex]\boxed{ \ 1.4 \times 10^{18} \ cm^3 \ }[/tex]
Given that we find in a reference book that the volume of all the oceans is 1.4 x 10⁹ km³.
To find the mass, we can use the density of water, also found in this reference book.
Firstly, we must convert the volume to cubic meters.
So, we have to convert the cubic kilometers to cubic meters.
From stair step conversion method, especially in cubic, each down one level must be multiplied by one thousand. We observe that from km³ to m³ down three steps, so
[tex]\boxed{ \ 1 \ km^3 = 1,000 \times 1,000 \times 1,000 \ cm^3 \ }[/tex]
[tex]\boxed{ \ 1 \ km^3 = 1,000,000,000 \ cm^3 \ }[/tex]
[tex]\boxed{ \ 1 \ km^3 = 10^9 \ cm^3 \ }[/tex]
Or we make it more practical to be as follows:
[tex]\boxed{ \ n \ steps \ multiplied \ or \ divided \ by 10^{3n} \ }[/tex]
The steps to convert km³ to cm³ are repeated like this,
[tex]\boxed{ \ 1 \ km^3 = 1 \times 10^{3(3)} \ cm^3 \ }[/tex]
[tex]\boxed{ \ 1 \ km^3 = 10^9 \ cm^3 \ }[/tex]
Let us convert the volume of 1.4 x 10⁹ km³ to cubic meters.
[tex]\boxed{ \ 1.4 \times 10^9 \ km^3 = ? \ cm^3 \ }[/tex]
[tex]\boxed{ \ 1.4 \times 10^9 \ km^3 = 1.4 \times 10^9 \times 10^{3(3)} \ cm^3 \ }[/tex]
[tex]\boxed{ \ 1.4 \times 10^9 \ km^3 = 1.4 \times 10^9 \times 10^9 \ cm^3 \ }[/tex]
[tex]\boxed{ \ 1.4 \times 10^9 \ km^3 = 1.4 \times 10^{18} \ cm^3 \ }[/tex]
Once converted, the volume of all oceans is obtained, i.e.,
[tex]\boxed{ \ 1.4 \times 10^{18} \ cm^3 \ }[/tex]
Note:
[tex]\boxed{ \ \chi^{ab} \rightleftharpoons \chi^{a \times b} \ }[/tex]
[tex]\boxed{ \ \chi^{a} \times \chi^{b} \rightleftharpoons \chi^{a + b} \ }[/tex]
To continue in calculating mass (m) based on density (ρ) and volume (V), use the formula:
[tex]\boxed{ \ \rho = \frac{m}{V}\ \rightarrow m = \rho \times V }[/tex]
Keywords: Suppose, in a reference book, the volume of all the oceans, is 1.4 × 10⁹ km³, the mass, the density of water, convert the volume to cubic meters, stair step conversion method, multiplied by, divided, drops
The mass of the ocean is [tex]\boxed{1.4 \times {{10}^{21}}{\text{ kg}}}[/tex] and the volume of the ocean is [tex]\boxed{1.4 \times {{10}^{18}}{m^3}}.[/tex]
Further explanation:
The relation between mass, density and volume can be expressed as follows,
[tex]\boxed{\rho = \frac{m}{v}}[/tex]
Here, [tex]\rho[/tex] is the density, [tex]m[/tex] is the mass and [tex]v[/tex] is the volume.
Given:
The volume of all the oceans is [tex]1.4 \times {10^9}{\text{ k}}{{\text{m}}^{\text{3}}}.[/tex]
Explanation:
The volume of the ocean in cubic meters can be expressed as follows,
[tex]\begin{aligned}{\text{Volume}} &= 1.4 \times {10^9}{\text{ k}}{{\text{m}}^{\text{3}}}\\&= 1.4 \times {10^9} \times {\left( {1000{\text{ m}}} \right)^3}\\&= 1.4 \times {10^9} \times {10^9}{\text{ }}{{\text{m}}^3}\\&= 1.4 \times {10^{18}}{\text{ }}{{\text{m}}^3}\\\end{aligned}[/tex]
Density of the water is [tex]1000{\text{ kg/}}{{\text{m}}^{\text{3}}}.[/tex]
The mass of the water can be obtained as follows,
[tex]\begin{aligned}\rho&= \frac{m}{v}\\1000&= \frac{m}{{1.4 \times {{10}^{18}}}}\\1.4\times {10^{18}} \times 1000 &= m\\1.4\times {10^{21}} &= m\\\end{aligned}[/tex]
The mass of the ocean is [tex]\boxed{1.4 \times {{10}^{21}}{\text{ kg}}}[/tex] and the volume of the ocean is [tex]\boxed{1.4 \times {{10}^{18}}{m^3}}.[/tex]
Learn more:
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Mensuration
Keywords: density, volume, oceans, water, density of water, the mass, mass, volume in cubic meters, cubic meters, kilogram, volume of oceans, convert.
