The base of a solid right prism of height 10 cm is a square and its volume is 160 cm3. What is its total surface area of the prism (in cm2)?
1. 176
2. 200
3. 192
4. 180
1. 176
2. 200
3. 192
4. 180
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Correct Answer – Option 3 : 192
Given :-
Base of prism is square
Height of prism = 10 cm
Volume of prism = 160 cm3
Concept :-
Concept of prism is based on cylinder
Total surface area of prism = Curved/lateral surface area + (2 × Base area)
Volume of prism = Base area × height
Curved surface area of prism = Base perimeter × Height
Area of square = side2
Perimeter of square = 4 × side
Calculation :-
⇒ 160 = Base area × 10
⇒ Base area = (160/10)
⇒ Base area = 16 cm2
As base of prism is square so,
⇒ 16 = side2
⇒ Side = √16 = 4 cm
⇒ Perimeter of base = 4 × 4 = 16 cm
Now
⇒ Curved surface area = 16 × 10 = 160 cm2
⇒ Total surface area = 160 + (2 × 16)
⇒ Total surface area = 160 + 32 = 192 cm2
∴ Total surface area is 192 cm2