Question

a liquid covers approximately 30% of a planets surface. assume the planet is a sphere with diameter about 8100 km. what amount of the planets surface is covered with the liquid? of the planets surface is covered with the liquid. (type an exact answer, using π as needed.)

Explanation:

Step1: Calculate the radius of the sphere

The diameter \(d = 8100\) km. The radius \(r=\frac{d}{2}=\frac{8100}{2}=4050\) km.

Step2: Find the surface area of the sphere

The surface area formula of a sphere is \(S = 4\pi r^{2}\). Substitute \(r = 4050\) into the formula: \(S=4\pi\times(4050)^{2}=4\pi\times16402500 = 65610000\pi\) \(km^{2}\).

Step3: Calculate the area covered by the liquid

The liquid covers \(30\%\) of the surface area. So the area \(A = 0.3\times S\). Substitute \(S = 65610000\pi\) into the formula: \(A=0.3\times65610000\pi=19683000\pi\) \(km^{2}\).

Answer:

\(19683000\pi\) \(km^{2}\)