The phenomenon of finite time extinction of bounded and non-negative solutions to the diffusion equation with strong absorption $\partial_t u - \Delta u^m + |x|^\sigma u^q = 0$, $(t,x)\in (0,\infty)\times\mathbb{R}^N$ with $m\ge 1$, $q \in (0, 1)$ and $\sigma> 0$, is addressed. Introducing the critical exponent $\sigma^* := 2(1 − q)/(m − 1)$ for $m > 1$ and $\sigma^* = \infty$ for m = 1, extinction in finite time is known to take place for $\sigma\in [0,\sigma^*)$ and an alternative proof is provided therein. When $m > 1$ and $\sigma \ge \sigma^*$, the occurrence of finite time extinction is proved for a specific class of initial conditions, thereby supplementing results on non-extinction that are available in that range of $\sigma$ and showing their sharpness.