Bank America Corp. reported continued earnings growth in the third quarter yesterday and said its total assets topped $100 billion for the first time.

The corporation, parent of the world's largest commercial bank, Bank of America, said a substantial increase in the volume of earning assets, particularly loans, helped boost its earnings in the quarter.

Bank America said its assets reached $104.4 billion on Sept. 30, an increase of 17.2 percent over the $89.1 billion reported a year earlier.

Third-quarter net income this year was $163.4 million ($1.12 a share) compared with $147.3 million ($1.01) for the third quarter of 1978, Nine-month net income was $442.6 million ($3.03) compared with $378.1 million ($2.52) for the same period of 1978. Net income and income before securities transactions for the nine-month and third-quarter periods were the same both, the company said.

Hit by escalating fuel costs and price wars on some key routes, two major airlines reported sharply lower third-quarter earnings.

Trans World Corp., the parent of Trans World Airlines, said earnings dropped 52 percent in the period. American Airlines reported a 97 percent decline.

Trans World said profits were $41.4 million ($2.28 a share), down from $86.8 million ($5.10) in last year's third quarter. Revenues rose to $1.29 billion from $1.06 billion.

American Airlines said its profit dropped to $2.8 million from $90.1 million in the same quarter last year. After subtracting preferred stock dividends, the company reported a loss of one cent a share for the quarter, down from a profit of $3.04 a share last year. Revenues rose to $855.5 million from $772.5 million.

For the first nine months, American reported profits of $91.2 million ($2.86), down from $127.1 million ($4.12) in the same period of 1978. Revenues rose to $2.4 billion from $2.1 billion.

Trans World said its nine-month profits were $52.4 million ($2.57), down from $98.7 million ($5.49). Revenue rose to $3.26 billion from $2.78 billion.

Four major companies involved in the manufacturing and selling of diversified lines of fibers, chemicals and plastics all reported strong earnings increases in the third quarter.

Most of the companies, however, said shipments to the automotive and steel industries were sagging.

Celanese Corp. said strong demand in its chemicals and cellulosic fibers units spurred a 10 percent increase in net income for the quarter. The company said it earned $37 million ($2.47 a share) compared with $33 million ($2.24) in the comparable 1978 quarter. Sales rose to $778 million from $650 million in the third quarter of last year.

For the first nine months, Celanese earned $114 million ($7.67) compared with $77 million ($5.25). Sales increased to $2.3 billion from $1.9 billion.

Monsanto Co. said its sales for the third quarter rose 26 percent to $1.5 billion from $1.19 billion for the third quarter of 1978.

Net income soared 111 percent to $98.9 million ($2.73 a share) from $46.8 million ($1.28) for the third quarter of 1978.

For the first nine months of 1979, sales reached $4.65 billion, an increase of 25 percent over sales of $3.71 billion for the first nine months of 1978. Net income was $320.2 million ($8.81) compared with $258.6 million ($7.08) for the first nine months of 1978.

Du Pont Co. reported earnings of $1.72 a share for the third quarter of this year, boosted by overseas sales.

The third-quarter per-share earnings -- which included a 12-cent-a-share benefit from a recent change in the United Kingdom tax laws -- were 21 percent above the $1.59-a-share second earned in the same period for 1978.

Net income for the quarter was $252 million compared with $208 million in the third quarter of 1978 and $233 million in the second quarter of this year.

Third-quarter sales of $3.13 billion were up 19 percent from $2.63 billion in the third quarter of 1978 but declined about 3 percent from the second quarter, in part because of a normal summer slowdown and the automotive industry's financial problems.

Union Carbide Corp. said its third-quarter earnings rose a hefty 85 percent to $149.4 million (2.27 a share) from $80.7 million ($1.25) in the 1978 third period. Sales were $2.33 billion, up to 18 percent from $1.98 billion.

The company said 1979 third-quarter earnings included a nonrecurring gain of $10.8 million (16 cents), reflecting a reduction of accrued deferred United Kingdom taxes.

Nine-month profits were $424.5 million (6.48) on sales $6.78 billion compared with $266.4 million ($4.12) a year earlier on sales of $5.78 billion.

Eastman Kodak Co. reported increases of 14 percent in sales and 20 percent in earnings during the third quarter compared with the same quarter of 1978.

The giant photographic concern said it earned $285.9 million ($1.78 a share) compared with $238.1 million ($1.48) in the comparible 1978 quarter. Sales rose to $2 billion from $1.75 billion.

For the first nine months of the year, Kodak reported sales of $5.44 billion compared with $4.7 billion for the same period in 1978. Net income totaled $706.1 million ($4.38) compared with $570.9 million ($3.54).

Kraft Inc., the food giant whose products include dairy and processed food reported a 24.2 percent gain in third-quarter earnings on a sales rise of 16.1 percent.

Third-quarter net income was $58.42 million ($2.08 a share) on net sales of $1.689 billion, up from $47.04 million ($1.68) on net sales of $1.455 billion for the corresponding quarter last year.

Draft also announced a 15.8 percent rise in profits for the first nine months on a sales gain of 13.9 percent.

Net income totaled $162.43 million ($5.79) on net sales of $4.808 billion against $143.31 million ($5.01)on net sales of $4.223 billion a year earlier.

Time Inc. announced that its revenues grew about twice as fast as net income in the third quarter.

The diversified publisher, which owns the Washington Star said earnings for the latest quarter totaled $31.85 million, up about 22.5 percent from the $26.01 million earned in the comparable quarter last year. Revenue jumped about 52.5 percent from $407.7 million to $621.4 million.

The number of shares outstanding, fully diluted, rose from 21.6 million a year ago to 27.95 million in the latest quarter. Earnings per share therefore, fell from $1.20 to $1.14.

For the first nine months, Time Inc. reported net income of $100.8 million ($3.61 a share), compared with $88.65 million ($4.10) in the first nine months of 1978. The 1978 figures include an extraordinary gain of $6.7 million (30 cents). Revenue in the latest three quarters rose to $1.79 billion from $1.16 billion a year ago.

The nine-month earnings include the results of Inland Container Corp. and American Television Communications Corp., which were acquired last November.