Question: Earth is approximately a sphere of radius$6.37\times {10}^{6}m$. What are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?

The radius of the Earth,$=6.37\times {10}^{6}m$

A system of units is a set of units in which units are represented in terms of some fundamental units. In SI system of units, there are seven fundamental units.

The expression for the circumference is given as follows:

$C=2\pi R$ … (i)

The expression for the surface area of sphere is given as follows:

$A=4\pi R^2$ … (ii)

The expression for the volume of sphere is given as follows:

$V=\frac{4\pi R^3}{3}$ … (iii)

Convert the radius of the Earth from meter to kilometer.

$$\begin{gathered} R=6.37\times {10}^{6}m \\ =6.37\times {10}^{6}m\times \frac{1km}{1000m} \\ =6.37\times {10}^{3}km \end{gathered}$$

Substitute the value of R in equation (i).

$$\begin{gathered} C=2\pi R \\ =2\times 3.14\times 6.37\times {10}^{6}m \\ =4.00\times {10}^{4}km \end{gathered}$$

Thus, the circumference of the Earth is $4.00\times {10}^{4}km$.

$$\begin{gathered} \text{Usingequation(ii),thesurfaceareaofEarthiscalculatedas:} \\ A=4{\mathrm{\pi R}}^2 \\ =4\times 3.14\times (6.37\times {10}^3) \\ =5.10\times {10}^8{\mathrm{km}}^2 \\ \text{Thus,thesurfaceareaoftheEarthis}5.10\times {10}^8{\mathrm{km}}^2\text{.} \end{gathered}$$

$$\begin{gathered} \text{Usingequation(iii),thevolumeoftheEarthiscalculatedas:} \\ V=\frac{4\pi R^3}{3} \\ =\frac{4\times 3.14\times (6.37\times {10}^{3}km)}{3} \\ =1.08\times {10}^{12}km \\ \text{Thus,thevolumeoftheEarthis}1.08\times {10}^{12}km\text{.} \end{gathered}$$