A hemispherical basin of 150 cm diameter holds water 120

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A hemispherical basin of 150 cm diameter holds water 120 times as much as a cylindrical tube. If the height of the tube is 15 cm, then the diameter of the tube is ?

1. 27 cm
2. 24 cm
3. 25 cm
4. 26 cm

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