Volume of sphere

How many times does the volume of a sphere increase if its radius increases 2 ×?

Correct answer:

n₂ =  8

Step-by-step explanation:

$$\begin{gathered} n_1=2 \\ {r}_1=1 \\ {r}_2=n_1\cdot r_1=2\cdot 1=2 \\ {V}_1={\displaystyle \frac{4}{3}}\cdot \pi \cdot r_1^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 1^3\doteq 4.1888 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r_2^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 2^3\doteq 33.5103 \\ {n}_2=V_2\mathrm{/}{V}_1=33.5103\mathrm{/}4.1888=8 \\ \text{ Verifying Solution: } \\ {n}_2=n_1^3=2^3=8 \end{gathered}$$

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