Statement-1: Extraction of zinc from sphalerite ore involves roasting followed by reduction with coke. 

Statement-2: Zinc can be extracted by hydrometallurgy.

Statement 1 is true “

The main ore of zinc is sphalerite . It mostly consists of crystalline zinc sulfide, but it almost always contains varying iron.

Roasting is followed by carbon reduction and zinc electro-fining for zinc extraction.

Statement 2 is incorrect,

The hydrometallurgy method involves adding more electropositive metal to the solution to draw the required metal out of it. But very few metals are more electro-positive than Zn, thus hydrometallurgy cannot be used to extract it.

Hence, option C is correct.