Sphere — If the radius of a sphere is doubled, by what percentage does its volume increase?

Introduction / Context:
Volume of a sphere V = (4/3) * π * r^3. If radius scales by factor k, the volume scales by k^3.

Given Data / Assumptions:

• r → 2r
• V ∝ r^3

Concept / Approach:
Doubling r gives V' = (4/3)π(2r)^3 = 8 * (4/3)πr^3 = 8V. An 8× total equals a 700% increase.

Step-by-Step Solution:
Increase factor = 8Percentage increase = (8 − 1) * 100% = 700%

Verification / Alternative check:
Scaling: cubic dependence makes volume grow faster than surface area when radius increases.

Why Other Options Are Wrong:
100% and 200% are too small; 800% implies 9×; 300% implies 4× total, not correct.

Common Pitfalls:
Using square (area) scaling instead of cube (volume) scaling.

Final Answer:
700 %