Additional District and Sessions Judge Yogesh Pareek convicted Lochan Srivas, a resident of Bajrang Para locality, and awarded him capital punishment, Deputy Director (Prosecution) Kripal Singh Gavaskar said.
Terming the offence as "rarest of the rare", the judge said the convict is a threat not only to the society but to humanity.
On February 24, Srivas took the girl, who was playing in the locality, to his house and raped her, the prosecution said.
The accused then strangled her, kept the child's body in a sack and threw it in Sangitarai area, Gavaskar said.
Following the victim's mother's complaint, the accused was arrested on the charges of rape and murder and chargesheet was filed in court on April 26, he said.
After hearing the arguments, the judge in his 58-page order convicted Srivas under sections 377 (unnatural sex), 302 (murder), 363 (punishment for kidnapping) of IPC, besides section 6 of Protection of Children from Sexual Offences (POCSO) Act, Gavaskar said.
The judge imposed a fine of�Rs�8,500 on him, and if he fails to pay the amount, he would have to undergo additional imprisonment of one-and-a-half years, Gavaskar said.
The court also directed the state government to pay compensation of Rs 5 lakh to the kin of the deceased after the period allowed for appeal by the convict ends, he added.