Math Olympiad Test: Surface Area and Volume- 2 - Class 9 MCQ

Curved surface area of pillar = 264 
⇒ 2πrh = 264 
Volume of pillar = 396 
⇒ πr²h = 396
∴ 

∴ 2πrh = 264
Now

The volume of the cone = 1232 
⇒ 1/3 πr²h = 1232


= 24 cm 
Slant height = l

 Let radius be r and height be h.
New radius be r/3 and height H. 
∴ 

Length will become 9 times.

Volume of the cube = 512 
⇒ a³ = 512 = 8³
⇒ a = 8
∴ Total surface area = 6a² = 6 × 8²
= 6 × 64  = 384 cm²

Number of cones

= 3 × 3 × 3 × 5 × 10 × 10
= 135 × 100
= 13500

No. of cones

= 3 × 21 × 2 = 126

Cone and hemisphere have equal base means equal radii, of R cm, 
Height of the cone be H cm
Height of hemisphere = R cm
Volume of cone = volume of hemisphere 

H/R = 2/1

No. of lead shots

= 168000

Radius of roller = 84/2 = 42cm
h = 100cm
Area covered by the roller in 200 
Revolutions = 200 × 2πrh

= 4 × 22 × 6 
= 88 × 6 = 528 m²

Here 2πrh = 264 m²
and  πr²h = 924 m³
∴ 

∴ Putting    r = 7
2πrh = 264
then 

Length of the tape = 4 (l + b + h) 
= 4 (30 + 25 + 25)
= 4 × 80 = 320 cm. 

Edge of each cube = 3 m
Volume of each cube = (3)³ = 27 m³
Volume of the cuboid = 18 × 12 × 9 = 1944 m³
Therefore, number of cubes = 1944/27​ = 72

Volume of the water accumulated the reservoir 18 hours = (120 × 75 × 2.4) m³
Let speed of water = v km/hour. 
The width of cuboid = b = 20/100 = 1/5 m
Height = h = 20/100 = 1/5 m
Length of water cuboid formed in 18 hours
= 18 v km = 18 × 1000 v m 
= 18000 v m
Volume of the water accumulated in reservoir in 18 hours 

⇒ 720 v = 120 × 75 × 2.4 

Let r be the inner radius of the cylinder
r = 12cm
Outer radius = R = 12 + 2 = 14cm 
h = 35cm 
Volume of wood = π (R² – r²) h

Curved surface area
= 1/3 × total surface area
= 1/3 × 462 = 154 
⇒ 2πrh = 154 …(1)
Total surface area = 462 
⇒ 2πrh + 2πr² = 462 
⇒ 154 + 2πr² = 462 
⇒ 2πr² = 308 

Putting this value in (i), we get
2πrh = 154 

∴  Volume of cylinder