State Health Secretary Nila Mohanan said 32 persons from Mangor Hill locality of Vasco, which has been declared as a containment zone, were among those who tested positive during the day.
The other eight had arrived in Goa from outside, she added.
The coastal state now has 109 active cases.
1,484 samples were sent for testing on Thursday, Mohanan said.
"Local administration has taken over the supplies of essential commodities (in containment zone). Pre-packed vegetables are also being supplied to the people in this zone," Mohanan added.
"Arrangements have been made by local municipality to collect the garbage. Leaflets are circulated to every household listing out the precautions to be taken by the people in containment zones," she added.
Goa's COVID-19 figures are as follows: Positive cases: 166, new cases: 40, deaths: nil, discharged: 57, active cases 109, Samples tested to date: 25,809. RPS KRK KRK