The base of a right prism, whose height is 2 cm, is a square. If the total surface area of the prism is 10 cm2, then its volume is:

Let side of base = $$a$$ cm and height = $$h=2$$ cm

Total surface area of prism = Curved surface area + (base+top) area

=> $$10$$ = Perimeter of base $$\times$$ height + $$2\times$$ area of base

=> $$(4\times a\times2)+(2\times a^2)=10$$

=> $$a^2+4a-5=0$$

=> $$a^2+5a-a-5=0$$

=> $$a(a+5)-1(a+5)=0$$

=> $$(a+5)(a-1)=0$$

=> $$a=1$$      $$[\because a$$ cannot be negative.$$]$$

$$\therefore$$ Volume = Base area $$\times$$ height 

= $$(1)^2\times2=2$$ $$cm^3$$

=> Ans - (C)