Let ABCDEF be a prism whose base is a right angled triangle, where sides adjacent to $$90^{\circ}$$ are $$9$$ cm and $$12$$ cm. If the cost of painting the prism is Rs. 151.20, at the rate of 20 paise per sq cm then the height of the prism is:

Cost of painting the prism at 20 paise per cm sq. = Rs. 151.20

=> Total surface area of prism = $$151.20\times\frac{100}{20}=756$$ $$cm^2$$

Let height of prism = $$h$$ cm

Hypotenuse of right angled triangle = $$h=\sqrt{l^2+b^2}$$

=> $$h=\sqrt{(9)^2+(12)^2}$$

=> $$h=\sqrt{81+144}=\sqrt{225}=15$$ cm

Thus, perimeter of base = $$9+12+15=36$$ cm --------------(i)

Area of base = $$\frac{1}{2}\times9\times12=54$$ $$cm^2$$ --------------(ii)

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

=> $$756$$ = Perimeter of base $$\times$$ height + $$2\times$$ area of base

=> $$(36\times h)+(2\times54)=756$$

=> $$36h=756-108$$

=> $$h=\frac{648}{36}=18$$ cm

=> Ans - (B)