Base of a prism of height 10 cm is square. Total surface area of the prism is 192 sq. cm. The volume of the prism is

Given,

Height of the square based prism (h) = 10 cm

Let the length of the side of the square base = a

Total surface area of the prism = 192 sq cm

$$=$$>  2a$$^{2}$$ + 4ah = 192

$$=$$>  a$$^{2}$$ + 2a(10) = 96

$$=$$>  a$$^{2}$$ + 20a - 96 = 0

$$=$$>  a$$^{2}$$ + 24a - 4a - 96 = 0

$$=$$>   a(a+24) - 4(a+24)=0

$$=$$>   (a+24)(a-4) = 0

$$=$$>   a+24 = 0   or   a-4 = 0

$$=$$>   a = -24    or    a = 4

a cannot be negative

$$=$$>  a = 4 cm

$$\therefore\ $$Volume of the Prism = Area of base x Height of the prism = a$$^{2}$$ x h = 4$$^{2}$$ x 10 = 16 x 10 = 160 cm$$^{2}$$

Hence, the correct answer is Option D