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The radius of the Earth is about
6.3 ×10^(3)km. Find its volume in terms of
pi.

The radius of the Earth is about $6.3 \times 10^{3} \mathrm{~km}$ . Find its volume in terms of $\pi$ .

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Volume of cylinders

Full solution

Q. The radius of the Earth is about

6.3 \times 10^{3} \mathrm{~km}

. Find its volume in terms of

\pi

.

Plug Radius into Formula: We know the formula for the volume of a sphere (Earth is approximately spherical) is $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere. We are given the radius of the Earth as $6.3 \times 10^3$ km. Let's plug this value into the formula.
Calculate Radius Cubed: First, we calculate $r^3$ (the radius cubed). The radius is $6.3 \times 10^3 \, \text{km}$ . $\newline$ $(6.3 \times 10^3 \, \text{km})^3 = 6.3^3 \times (10^3)^3 = 250.047 \times 10^9 \, \text{km}^3$
Substitute into Volume Formula: Now, we substitute the value of $r^3$ into the volume formula. $\newline$ $V = \left(\frac{4}{3}\right)\pi(250.047 \times 10^9 \text{ km}^3)$
Simplify Constants: We can simplify this by multiplying the constants and keeping $\pi$ in the expression. $V = \left(\frac{4}{3}\right) \times \pi \times 250.047 \times 10^9$ km $^3$
Multiply Numerical Values: Multiplying the numerical values together, we get: $\newline$ $V \approx \frac{4}{3} \times \pi \times 250.047 \times 10^9 \, \text{km}^3$ $\newline$ $V \approx 333.396 \times \pi \times 10^9 \, \text{km}^3$
Write Volume in Scientific Notation: We can write the volume in scientific notation for clarity: $\newline$ $V \approx 3.334 \times 10^2 \times \pi \times 10^9 \text{ km}^3$ $\newline$ $V \approx 3.334 \times \pi \times 10^{2+9} \text{ km}^3$ $\newline$ $V \approx 3.334 \times \pi \times 10^{11} \text{ km}^3$

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