If the Earth has a radius of 6378 km and the dwarf planet Pluto a radius of 1187 km, what is the approximate Pluto to Earth surface area-to-volume ratio?
A) 0.19
B) 7.5
C) 5.4
D) 2.1

Question

Quizplus · Accepted Answer

The formula for surface area of a sphere is 4πr² and the formula for volume is (4/3)πr³.

For Earth:
Surface area = 4π(6378)² = 510,072,000 km²
Volume = (4/3)π(6378)³ = 1.08 x 10¹² km³

For Pluto:
Surface area = 4π(1187)² = 17,646,248 km²
Volume = (4/3)π(1187)³ = 6.39 x 10¹¹ km³

The ratio of surface area to volume for Pluto is:
17,646,248 / 6.39 x 10¹¹ ≈ 0.0276 km²/km³

The ratio of surface area to volume for Earth is:
510,072,000 / 1.08 x 10¹² ≈ 0.472 km²/km³

The ratio for Pluto is approximately 5.4 times smaller than that of Earth, so the best answer is C) 5.4.

If the Earth Has a Radius of 6378 Km and the Dwarf