Let level of water will be increased by h cm
π x (15)² x h = (4/3)π(10)³

Correct Option: D

Let level of water will be increased by h cm
π x (15)² x h = (4/3)π(10)³
∴ h = [(4/3) x 10 x 10 x 10] / [15 x 15]
= 5²⁵/₂₇ cm

Given, radius of pipe 5/2 x 10 = 5/20 cm [∵ 1 cm = 10 mm]
Height of pipe = 1000 cm
Radius of vessel = 20 cm and height = 24 cm
Volume of water flow in one minute from cylindrical pipe = π (5/20)² x 1000
= 125/2 π cm³
and volume of conical vessel = 1/3 π(20)² x 24 = 3200π cm³
∴ Required time = (3200π x 2) / 125π

Correct Option: A

Given, radius of pipe 5/2 x 10 = 5/20 cm [∵ 1 cm = 10 mm]
Height of pipe = 1000 cm
Radius of vessel = 20 cm and height = 24 cm
Volume of water flow in one minute from cylindrical pipe = π (5/20)² x 1000
= 125/2 π cm³
and volume of conical vessel = 1/3 π(20)² x 24 = 3200π cm³
∴ Required time = (3200π x 2) / 125π
= 51¹/₅ or 51 min 12 s

1 hec = 10000 m³
Volume of water = Base area x Height

Correct Option: C

1 hec = 10000 m³
Volume of water = Base area x Height
= (10000 x 10)/100 = 1000 m³

Given, 4πr² = 2πrh
∴ h = 2r
Now, required ratio
= 4/3πr³ : πr²h

Correct Option: B

Given, 4πr² = 2πrh
∴ h = 2r
Now, required ratio
= 4/3πr³ : πr²h
= 4r : 3h
= 4r : 6r [ ∴ h = 2r]
= 2 : 3

Volume of 1 bullet = 4/3π(2)³ = (32/3 x 22/7) cm³
Volume of the cube = (44)³

Correct Option: B

Volume of 1 bullet = 4/3π(2)³ = (32/3 x 22/7) cm³
Volume of the cube = (44)³
∴ Number of bullets = Volume of solid/Volume of 1 bullet
= (44)³ x 3 x 7 / 32 x 22 = 2541