Answer
a) $5.15\times10^{14}\text{ m}^2$
b) $3.605\times10^{14}\text{ m}^2$
c) $1.37\times10^{18}\text{ m}^3$
Work Step by Step
a) Using the given formula for the surface area of a sphere, with $r=6.4\times10^6$, then
$$\begin{aligned}
S.A.&=4\pi r^2
\\&=
4\pi(6.4\times10^6)^2
\\&=
4\pi(40.96\times10^{12})
\\&\approx
514.72\times10^{12}
\\&\approx
5.1472\times10^2\times10^{12}
\\&\approx
5.15\times10^{14}
.\end{aligned}$$Hence, the surface area, $S.A.$, of the Earth is approximately $5.15\times10^{14}\text{ m}^2$.
b) Since oceans cover about $70\%$ of the surface area of the Earth, then
$$
0.70(5.15\times10^{14})=3.605\times10^{14}
.$$Hence, the earth's surface is covered by approximately $3.605\times10^{14}\text{ m}^2$ of water.
c) Multiplying the surface area of the oceans by the given depth results in
$$\begin{aligned}
\left(3.605\times10^{14}\right)(3790)&=
13662.95\times10^{14}
\\&=
1.366295\times10^4\times10^{14}
\\&=
1.366295\times10^{18}
\\&\approx
1.37\times10^{18}
.\end{aligned}$$Hence, the volume of water in the Earth's oceans is approximately $1.37\times10^{18}\text{ m}^3$.
