Math Olympiad Test: Surface Area and Volume- 3 - Class 10 MCQ

Since, Δ OAB ~ Δ OCD

⇒ CD = 3 cm
Slant height of cone (/) = 
= 15 cm
Curved surface area of the conical pot will be S = π × r × l = 135π cm²
Let l' be the slant height occupied by water of depth h' = 4cm
So l'/l = h'/h
⇒ l' = 4/12 × 15 = 5cm
Hence radius of water cone 
r' = √(l'² - h'²)=√(5² - 4²) = 3cm
Curved surface area of water cone 
= π × r' × l' = 15π
So area of interior surface of the cone not in contact with water will be
= (135 - 15)π cm² = 377.14 cm²

Volume of frustum/bucket = 

= 

= 48510 cm³

Let the radius of the cylinder be 2/3 diameter
So, diameter of the cylinder = 2r
∴ Height of the cylinder = 2/3(2r) = 4r/3
Volume of the cylinder = Volume of the sphere of radius 4 cm
⇒ 
⇒ r³ = 4³ ⇒ r = 4 cm.

Volume o f one solid sphere = 

Volume of cylinder = πr²h = π x 4 x 45

Now, Number of spheres x Volume of one sphere = Volume of cylinder

⇒ Number of spheres x 

⇒ Number of spheres = 45/9 = 5

Let OC = h and AB = r

Now, Δ OAB ~ Δ OCD

Volume of smaller cone = 1/27 (Volume of whole cone)

⇒ 

h³ = 10 x 10 x 10

⇒ h = 10 cm.

Required height, AC = 30 - 10 = 20 cm

Volume of cylindrical tank = πr²h

So, we need radius and height.
Radius can be found from either statement I or III and height from statement II.

To cut out maximum area, radius of the cone = radius of the hemisphere = r and height of the cone = radius of the hemisphere = r

∴ Volume of the cone = 1/3πr²h

= 1/3πr³

Radius of cylinder = Radius of cone = 14 m

Height of cylinder = 3 m

Height of cone = 10.5 m 

Slant height of cone

= 

Total curved surface area of tent = Curved surface area of cylinder + Curved surface area of cone

= π(2 x 14 x 3 + 14 x 17.5)

= 

Cost of painting the inner surface at the rate of ₹ 2 per m² = 2 x 1034 = ₹ 2068

Volume of bucket = 

= 

= 28490 cm³

∴ Volume of bucket = 28490 cm³ = 28.49 L

Total number of people = 150 
Space required for each person on the ground = 4 m² 
Area of base of the cone = 150 x 4
⇒ πr² = 600 ⇒ r² =  2100 /11
Volume of air required by 150 persons = 150 x 20.
⇒ 
⇒ 200h = 3000 ⇒ h = 15 m