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

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

Volume of water = Volume of conical flask = (1/3)πr²h
Now, the water is poured into cylindrical flask.
∴ Volume of cylinder = Volumes of water
⇒ π (mr)² x Height = (1/3)πr²h

Correct Option: C

Volume of water = Volume of conical flask = (1/3)πr²h
Now, the water is poured into cylindrical flask.
∴ Volume of cylinder = Volumes of water
⇒ π (mr)² x Height = (1/3)πr²h
∴ Height = h/3m²

Given, diameter = 150 cm
∴ r = 150/2 cm
According to the question,
2/3π (150/2)³ = 120 πr² x 15

Correct Option: C

Given, diameter = 150 cm
∴ r = 150/2 cm
According to the question,
2/3π (150/2)³ = 120 πr² x 15
⇒ (2/3) x 150 x 150 x 150 / 8 = 120 x 15 x r²
⇒ r² = (150 x 150 x 150) / (12 x 120 x 5)
⇒ r² = 625/4
⇒ r = √625/4 = 25/2
∴ Diameter = 2r = 2 x 25/2 = 25 cm

Let length of the wire be h According to the question,
Volume of sphere = Volume of wire
(4/3) x π x 18 x 18 x 18 = π x (2/10) x (2/10) x h

Correct Option: D

Let length of the wire be h According to the question,
Volume of sphere = Volume of wire
(4/3) x π x 18 x 18 x 18 = π x (2/10) x (2/10) x h
∴ h = (100 x 1944) cm
= (100 x 1944)/100 m = 1944 m [∵ 1 cm = 1/100 m]