1. **State the problem:** Find the volume of the sphere defined by the equation $$x^2 + y^2 + z^2 = a^2$$ using triple integration. 2. **Set up the integral:** The sphere is symmetric and can be described in spherical coordinates where $$x = \rho \sin\phi \cos\theta$$, $$y = \rho \sin\phi \sin\theta$$, $$z = \rho \cos\phi$$, with $$\rho$$ from 0 to $$a$$, $$\phi$$ from 0 to $$\pi$$, and $$\theta$$ from 0 to $$2\pi$$. 3. **Volume element in spherical coordinates:** The volume element is $$dV = \rho^2 \sin\phi \, d\rho \, d\phi \, d\theta$$. 4. **Write the triple integral for volume:** $$V = \int_0^{2\pi} \int_0^{\pi} \int_0^a \rho^2 \sin\phi \, d\rho \, d\phi \, d\theta$$ 5. **Integrate with respect to $$\rho$$:** $$\int_0^a \rho^2 \, d\rho = \left[ \frac{\rho^3}{3} \right]_0^a = \frac{a^3}{3}$$ 6. **Integrate with respect to $$\phi$$:** $$\int_0^{\pi} \sin\phi \, d\phi = \left[ -\cos\phi \right]_0^{\pi} = -\cos\pi + \cos0 = 2$$ 7. **Integrate with respect to $$\theta$$:** $$\int_0^{2\pi} d\theta = 2\pi$$ 8. **Combine all results:** $$V = 2\pi \times 2 \times \frac{a^3}{3} = \frac{4\pi a^3}{3}$$ **Final answer:** The volume of the sphere is $$\boxed{\frac{4}{3} \pi a^3}$$.