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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