Earth has a diameter of approximately 8000 miles. Jupiter's diameter is approximately 88000 miles. How many times greater is the volume of Jupiter than the volume of Earth?
Vj/Ve=(Dj/De)^3=(88000/8000)^3=11^3=1331
To calculate the ratio of Jupiter's volume to Earth's volume, we need to compare the cubes of their respective diameters. The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius. Since the diameter is twice the radius, we can use the formula V = (4/3) * π * (d/2)^3 for convenience.
The diameter of Earth is approximately 8,000 miles, so the radius is half of that, or 4,000 miles. Substituting this value into the formula, we have V_earth = (4/3) * π * (4000/2)^3 = (4/3) * π * 2000^3.
The diameter of Jupiter is approximately 88,000 miles, so the radius is half of that, or 44,000 miles. Substituting this value into the formula, we have V_jupiter = (4/3) * π * (44000/2)^3 = (4/3) * π * 22000^3.
Now, we can calculate the ratio of the volumes by dividing V_jupiter by V_earth:
Ratio = V_jupiter / V_earth
= [(4/3) * π * 22000^3] / [(4/3) * π * 2000^3]
= (22000^3) / (2000^3)
Simplifying the expression, we find:
Ratio = (22000 * 22000 * 22000) / (2000 * 2000 * 2000)
= 106 * 106 * 106 / 10 * 10 * 10
= 106 * 106 * 106 / 1000
Calculating the ratio, we find:
Ratio ≈ 1,106,096,000 / 1,000
≈ 1,106,096
Therefore, the volume of Jupiter is approximately 1,106,096 times greater than the volume of Earth.
To find the volume of a sphere, you need to use the formula V = (4/3) * π * r³, where V is the volume and r is the radius of the sphere.
Given that Earth's diameter is approximately 8,000 miles, we can calculate its radius by dividing the diameter by 2: r(Earth) = 8,000 / 2 = 4,000 miles.
Now, we can calculate Earth's volume: V(Earth) = (4/3) * π * (4,000)³.
Similarly, Jupiter's diameter is approximately 88,000 miles, so its radius is calculated as: r(Jupiter) = 88,000 / 2 = 44,000 miles.
Now, we can calculate Jupiter's volume: V(Jupiter) = (4/3) * π * (44,000)³.
To find how many times greater the volume of Jupiter is than the volume of Earth, we divide V(Jupiter) by V(Earth): ratio = V(Jupiter) / V(Earth).
Let's calculate the ratio.