Math Olympiad Test: Surface Area and Volume- 1 - Class 9 MCQ

Let l = 2b, h = 3m 
Area of four walls = 108 
2 (l + b) h = 108 
⇒ 2 (2b + b) 3 = 108 
⇒ 3b = 108/6 = 18
⇒ b = 18/3 = 6
∴ l = 2b = 2 × 6 = 12
∴ Volume of cold storage
= lbh = 12 × 6 × 3 = 216 m³

No. of bricks

Volume of cuboid = a³/2 = Ibh
∴ Surface area of each cuboid
= 2 (lb + bh + lh) 

= 2 (2a²) = 4a²
Total surface area of cube = 6a²
∴ Required ratio = 6a² : 4a² = 3 : 2

The curved surface area of the roller = 2πrh

= 44 × 150 × 6 
Area covered by roller in 100 revolutions 

Cost of leveling the playground

= ₹ 198

Volume of the cylinder = 448π
⇒ πr²h = 448π
⇒ r²h = 448 

⇒ r = 8 cm
Lateral surface area = 2πrh

= 22 × 16 = 352 cm²

Let the number of glasses be n
∴ Total volume in the vessel = volume of juice in glasses
⇒ πR²H = n × πr²h
⇒ R²H = nr²h
⇒ (15)² × 32 = n × (3)² × 8 
⇒ n = 5 × 5 × 4 = 100 

Curved surface = πrl = 22/7 × 7 × 25 = 550 m²
Length of canvas used

Let the diameter of the earth be x m
∴ Diameter of moon = x/4 m

The volume of water in the tank
= 150 × 100 × 3 = 45000 m³
Area of a cross-section of the pipe
= 2dm × 1.5dm 

Let the time taken be t hours. 
The volume of water that flows in a tank in t hours.

= 450 t m³
⇒ 450t = 45000 
⇒ t = 45000/450 = 100 hours  

Volume of water