Answer:
a.)   depth of the lake = (volume of the lake) / area of lake 
             = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet
b.) 11 inches  = 0.9167 feet
     Water gained in cubic feet gained by the lake 
          = 624,305,840,400  0.9167
  0.9167  
          = 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year 
       = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
       =  0.0033
       = 0.33% 
Step-by-step explanation:
i) acres to square feet :    1 acre = 43560 square feet
   therefore 14,332,090 acres  = 624,305,840,400 square feet
ii) 1 mile  = 5280 feet
    1 cubic mile  = 5280  5280
 5280  5280 = 147,197,952,000 cubic feet
 5280 = 147,197,952,000 cubic feet
 therefore 1180 cubic miles  = 173,693,585,360,000 cubic feet
 a.)   depth of the lake = (volume of the lake) / area of lake 
             = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet
b.) 11 inches  = 0.9167 feet
     Water gained in cubic feet gained by the lake 
     = 624,305,840,400  0.9167   = 572,282,434,719.5 cubic feet
  0.9167   = 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year 
   = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
    =  0.0033
   = 0.33%