# Earth is approximately a sphere of radius

Earth is approximately a sphere of radius 6.37 x 106 m.
What are
(a) its circumference in kilometers,
(b) its surface area in square kilometers,and
(c) its volume in cubic kilometers?

Solutions

(a) Its circumference in kilometers :

\begin{aligned}
C &= 2\pi r \\
&= 2\cdot \pi \cdot 6.37 \times 10^6 \\
&= 4.00 \times 10^7 \quad \textrm{m} \\
&= 4.00 \times 10^4 \quad \textrm{km}
\end{aligned}

(b) its surface area in square kilometers :
\begin{aligned}
A &= 4\pi r^2 \\
&= 4\cdot \pi \cdot (6.37 \times 10^6)^2 \\
&= 5.10 \times 10^{16} \quad \textrm{m}^2 \\
&= 5.10 \times 10^{10} \quad \textrm{km}^2
\end{aligned}

(c) its volume in cubic kilometers
\begin{aligned}
V &= \frac{4}{3}\pi r^3 \\
&= \frac{4}{3}\cdot \pi \cdot (6.37 \times 10^6)^3 \\
&= 1.08 \times 10^{21} \quad \textrm{m}^3 \\
&= 5.10 \times 10^{12} \quad \textrm{km}^3
\end{aligned}