Third-quarter profits of Citicorp, the nation's largest bank holding company, dropped 11 percent from their levels a year earlier, Citibank's parent company said yesterday.

Citicorp said its profits fell to $135 million ($1.07 a share) from $151 million ($1.21) in the comparable 1980 quarter.

Nine-month earnings of $338 million ($2.68) were down 18 percent from $411 million ($3.31) in the same period last year.

Citicorp attributed the lower earnings to "the continuing impact of high and volatile interest rates."

Manufacturers Hanover Corp., parent of the country's fourth-largest bank, said earnings climbed nearly 22 percent to $70.6 million from $58 million a year ago. Per-share earnings rose to $2.10 from $1.74.

For the nine months, Manufacturers Hanover earned $185.6 million ($5.52 a share), up nearly 9 percent from $170.7 million ($5.13).

Polaroid Corp.'s third-quarter earnings fell 69 percent from a year earlier on lower sales and losses from foreign currency translation, the company said yesterday.

Earnings for the three-month period were $6.3 million (19 cents a share) compared with $20.6 million (63 cents) in last year's third quarter. Sales fell 2 percent to $358.9 million from $364.7 million.

William J. McCune, president and chief executive of the photography giant, said the drop in earnings was mainly attributable to the dollar's strength on foreign exchange markets in relation to overseas currencies.

For the first nine months of the year, earnings fell 45 percent to $29.3 million (89 cents) from $53.1 million ($1.62) in the same period last year. Sales dropped 1.6 percent to $974.2 million from $990.2 million.

Monsanto Co. reported yesterday that third-quarter earnings were $123.6 million ($3.09 a share), up from $29.6 million (81 cents) during the same period last year.

The increase included a $67.7 million nonrecurring gain from the sale to Du Pont Co. of Monsanto's portion of a Monsanto-Conoco Inc. joint venture. Du Pont merged recently with Conoco.

Sales were $1.634 billion, up from $1.539 billion during the same period in 1980.

Nine-month net income was $393.4 million on sales of $5.389 billion compared with income a year earlier of $217 million on sales of $4.910 billion.

B.F. Goodrich Co. said yesterday that its third-quarter profits rose sharply from a year earlier.

The tire, rubber and chemical company said its third-quarter profits rose to $22.4 million ($1.11 a share) from $8.7 million (48 cents) in a year earlier. Sales were $822.2 million, up from $782.4 million.

Goodrich said its third-quarter profit included $8.7 million (44 cents) from divestments and the sale of its interest in its Yokohama Rubber subsidiary.

Nine-month earnings were $73.7 million ($3.76) on sales of $2.4 billion compared with earnings a year earlier of $39 million ($2.25) on sales of $2.3 billion.