Volume of a Sphere Math Example 4

Solution

1. 1
   Step 1: Original volume with radius $r$: $V_1 = \frac{4}{3}\pi r^3$.
2. 2
   Step 2: New volume with radius $2r$: $V_2 = \frac{4}{3}\pi (2r)^3 = \frac{4}{3}\pi \times 8r^3 = 8 \times \frac{4}{3}\pi r^3$.
3. 3
   Step 3: Find the ratio: $\frac{V_2}{V_1} = \frac{8 \times \frac{4}{3}\pi r^3}{\frac{4}{3}\pi r^3} = 8$.