  In this paper, we consider the Ma-Minda classes of analytic functions
$\mathcal{S}^{*}(\phi):= \{f\in \mathcal{A} : ({zf'(z)}/{f(z)}) \prec \phi(z)
\}$ and $\mathcal{C}(\phi):= \{f\in \mathcal{A} : (1+{zf''(z)}/{f'(z)}) \prec
\phi(z) \}$ defined on the unit disk $\mathbb{D}$ and show that the classes
$\mathcal{S}^{*}(1+\alpha z)$ and $\mathcal{C}(1+\alpha z)$, $0<\alpha \leq 1$
solve the problem of finding the sharp $\mathcal{S}^{*}(\phi)$-radii and
$\mathcal{C}(\phi)$-radii for some normalized special functions, whenever
$\phi(-1)=1-\alpha$. Radius of strongly starlikeness is also considered.
