The NYPD inspector killed when his motorcycle collided with a dump truck Monday morning in the Bronx was the commanding officer of the department’s Cadet Corps, police sources said.

Inspector Michael McGrath, who was off duty, was cruising south along East Tremont Avenue when he was struck by the truck as it turned left onto Waterbury Avenue around 8 a.m., sources said.

“He got cut off. He ended up rolling the motorcycle,” said one source of the crash, which remains under investigation. “He fell off and slid under the wheels of the [truck].”

McGrath, who spent half of his 56 years with the NYPD, was rushed to Jacobi Medical Center, but he succumbed to his injuries with his sister and adult daughter by his side, according to sources.

Captains Endowment Association president Roy Richter remembered McGrath as a cheerful, dyed-in-the-wool Finest who championed the Cadet Corps and the police academy.

“He’s the guy who always greets you with a smile,” said Richter. “He’s somebody that you don’t just rely on, but he’s actually part of the fabric of what makes the police department.

“He’s been charged with incredible responsibility and he’s come through over and over, including the academy project.”

The NYPD Cadet Corps allows college students to learn the ropes of the job under the eye of police academy instructors.