1. Combine the quinoa, water, pepper, and 1/4 teaspoon of the salt in a medium saucepan.
2. Bring to a boil over medium-high; cover and reduce the heat to low. Cook until all the liquid has been absorbed, about 16 minutes.
3. Fluff with a fork, and cool completely. (Spread the quinoa on a large plate or sheet pan to expedite the cooling time.)
4. Whisk together the lime juice, oil, cilantro, and remaining 1/2 teaspoon salt in a large bowl. Add the cooked quinoa, cucumber slices, radish slices, and arugula; toss to coat. Serve immediately.