Step 1: Use the inverse relation:
At constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure. The pressure rises by a factor of 3.5, so the volume must fall by the same factor.
Step 2: Divide:
$V_2 = \dfrac{10.0}{3.5}$ cm$^3$. Since $3.5 \times 2.86 = 10.01$, we get $V_2 \approx 2.86$ cm$^3$.
Step 3: Sanity check:
The new volume must be smaller than 10.0 cm$^3$. Only 2.86 and 0.286 are smaller, and 0.286 cm$^3$ would need a pressure of 35 atm, so B is right.
Final Answer:
Dividing 10.0 cm3 by 3.5 gives a final volume of 2.86 cm3.
\[ \boxed{\text{(B) }2.86\ \text{cm}^3} \]