Robert Whittier Dudley, 73, a lawyer by training who became a businessman in the Washington area and who was active in volunteer organizations, died of cancer Jan. 18 at Johns Hopkins Hospital in Baltimore. He lived in Bethesda.

Mr. Dudley was president and board chairman of the Consumers Gas Utility Co. of Huntington, W.Va., whose offices are in Washington. He also had been a director of the Presidential Savings Association of Bethesda, United Masonry Inc. of Alexandria, and the Custom Leasing Corp. of Lanham. He was a member of the boards of several mutual funds.

He was a trustee emeritus of the Holton-Arms School and past president of the House of Mercy, a charitable organization. He was a member of the Chevy Chase, Metropolitan, and Congressional Country clubs. His hobbies included tennis.

Mr. Dudley was born in Hanover, N.H. He was a graduate of the University of Wisconsin and earned a law degree at the University of Michigan. He moved to Washington after service with the Navy during World War II. He engaged in the private practice of law until the 1950s.

His first wife, the former Argentina Copello, whom he married in 1947, died in 1984. Mr. Dudley and Olga Hirshhorn, widow of Joseph Hirshhorn, the noted art patron, were married on Sept. 1, 1985.

In addition to his wife, of Bethesda, Mr. Dudley's survivors include six children by his first marriage, Robert W. Jr., of Escondido, Calif., Carol Louise Dudley of Los Angeles, Cynthia Dudley-Gaillard of Potomac, Nancy W. Dudley of Bethesda, Diana W. Dudley of Durham, N.C., and Suzanne C. Dudley of New York City; one sister, Constance D. Casey of Washington; two brothers, Charles M., of Lebanon, N.H., and Bernard F., of Naples, Fla., and two grandchildren.