You seem to be missing a few digits in the model number. Sears Parts Direct lists 11 refrigerator models that start 253.562824. (The full models numbers have 2 extra characters, including 253.56282400 and 253.5628240N.) See http://www.searspartsdirect.com/model/search.html?q=253.562824
for the list of models.
Kenmore uses the 3rd digit after the decimal point to indicate the cubic footage of their refrigerators. With a 2 in that position, this model has a 22 cubic feet capacity (probably 21.6 or 22.1 cubic feet before rounding). Using the size of other models, the external dimensions will be between 30" W x 31-3/4" D x 69" H (the size of a 21 cu. ft. model) and 35-5/8" W x 28-1/4" D x 69-3/8" H (23 cu. ft. model). One current Frigidaire 22 cubic foot side by side model has the external dimensions: 33" W x 32" D x 69-7/8" H. (Note: the 253 in the model number indicates a product made by Frigidaire for the Kenmore line.) Unfortunately, I can't find the dimensions for any of 253.562824 models.
I hope this helps.