1. 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:
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By: anil on 05 May 2019 02.28 am
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 $$ imes$$ height + $$2 imes$$ area of base => $$(4 imes a imes2)+(2 imes a^2)=10$$ => $$a^2+4a-5=0$$ => $$a^2+5a-a-5=0$$ => $$a(a+5)-1(a+5)=0$$ => $$(a+5)(a-1)=0$$ => $$a=1$$ $$[ecause a$$ cannot be negative.$$]$$ $$ herefore$$ Volume = Base area $$ imes$$ height = $$(1)^2 imes2=2$$ $$cm^3$$ => Ans - (C)
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