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SSC MTS 2024 PYQ — Question 7

SSC MTS - 08/10/2024 - (4:00 PM - 5:30 PM) • Quantitative Aptitude • Q7

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A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl is:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 60.

The volume of a hemisphere = 23πr3{2\over3}\pi r^3 = 23π(15)3{2\over3}\pi(15)^3

The volume of a cylinder = πr2h\pi r^2h = π(52)2×6\pi({5\over2})^2\times6

number of bottles(n) = 23π(15)3π(52)2h{2\over3}\pi(15)^3\over{\pi ({5\over2})^2h} = 23(15)3(52)2×6{2\over3}(15)^3\over{({5\over2})^2\times6} 

⇒ n = 23×3375254×6{2\over3}\times3375\over{{25\over4}\times6} = 2250×41502250\times4\over150

⇒ n = 60