Question

**PLS HELP THX** Write a word problem whose solution involves taking a cube root. State the problem and solve it, showing and explaining all steps.

Answer 1

The astronomer finds a planet orbiting a binary star with a mass of 2 solar masses, completing its orbit every 4 years. Using Kepler's third law, where a3 = M × P2, and with calculations, the semi-major axis is the cube root of 32 or about 3.2 AU.

Step-by-step explanation:

Word Problem Involving Cube Root

Imagine a small planet in a distant galaxy following Kepler's third law of planetary motion, where the square of the orbital period (P) is proportional to the cube of the semi-major axis of its orbit (a). Let's say an astronomer discovers a planet orbiting a star (similar to the Sun) with a mass (M) equal to 2 solar masses. If the planet completes an orbit every 4 years, what is the length of the semi-major axis of its orbit?

To solve this problem, we use the formula: a3 = M × P2. Here, M = 2 and P = 4, so:

a3 = 2 × 42 = 2 × 16 = 32

Now, to find the semi-major axis (a), we need to take the cube root of 32:

a = ∛32 ≈ 3.2 (AU - Astronomical Units)

Therefore, the semi-major axis of the planet's orbit is approximately 3.2 AU.

Answer 2

Imagine that we know the volume of the Earth, which is 1.08 x 10**12 km3

And we model the Earth as a perfect Sphere.

We know that the volume of the sphere is V = 4/3 * pi * (r**3)

We can solve for r......................r = cube root((V*3/4)/pi)

r = 6364,71 km , which is a good approximation for the radius of the Earth!