The curved dome has the area of half a sphere with radius 8 in. That is
... A = 2πr² = 2π(8 in)² = 128π in²
The lateral area of the cylinder is
... A = 2πrh = 2π(8 in)(7 in) = 112π in²
The area of the flat base is
... A = πr² = π(8 in)² = 64π in²
Then the total area of the figure is
... (128π + 112π + 64π) in² ≈ 304·3.14 in²
... = 954.56 in² . . . . matches the 2nd selection
