MATH SOLVE

5 months ago

Q:
# The radius of Jupiter is approximately 44,423 miles, and the radius of the Earth is approximately 3,960 miles. How many times larger is the volume of Jupiter than the volume of the Earth? Round your answer to the nearest whole number. A. 1,412 B. 11 C. 126 D. 4,090

Accepted Solution

A:

We can model both planets as a sphere.

We have then:

For the earth:

v1 = (4/3) * (pi) * (r1 ^ 3)

v1 = (4/3) * (pi) * ((3960) ^ 3)

For Jupiter:

v2 = (4/3) * (pi) * (r2 ^ 3)

v2 = (4/3) * (pi) * ((44423) ^ 3)

Dividing both equations we have:

v2 / v1 = ((44423) ^ 3) / ((3960) ^ 3)

v2 / v1 = 1411.685958

Rounding off we have:

v2 = 1412v1

Answer:

the volume of Jupiter is 1412 times larger than the volume of the Earth

A. 1,412

We have then:

For the earth:

v1 = (4/3) * (pi) * (r1 ^ 3)

v1 = (4/3) * (pi) * ((3960) ^ 3)

For Jupiter:

v2 = (4/3) * (pi) * (r2 ^ 3)

v2 = (4/3) * (pi) * ((44423) ^ 3)

Dividing both equations we have:

v2 / v1 = ((44423) ^ 3) / ((3960) ^ 3)

v2 / v1 = 1411.685958

Rounding off we have:

v2 = 1412v1

Answer:

the volume of Jupiter is 1412 times larger than the volume of the Earth

A. 1,412