Question : The base of the 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:
Option 1: 3 cm3
Option 2: 1 cm3
Option 3: 2 cm3
Option 4: 4 cm3
Correct Answer: 2 cm 3
Solution : Height = 2 cm The total surface area of the prism = 10 cm 2 Let the side of the base be $a$ cm. The total surface area of the prism = curved surface area + 2 × area of base 10 = perimeter of base × height + 2 × area of base ⇒ (4 × $a$ × 2) + (2 × $a^2$) = 10 ⇒ $a^2 + 4a -5$ = 0 ⇒ $(a+5)(a-1)$ = 0 Since $a$ cannot be negative, $a$ = 1 Volume = base area × height = $(1)^2 × 2$ = 2 cm 3 Hence, the correct answer is 2 cm 3 .
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