Question

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

Answer 1

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