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SSC MTS 2024 PYQ — Question 6

SSC MTS - 29/10/2024 - (4:00 PM - 5:30 PM) • Quantitative Aptitude • Q6

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The diameter of a hollow hemisphere is 30 cm. Water is filled in it up to its brim. When spherical lead shots each of radius 0.75 cm are dropped into the hemisphere, two-fifth of the water flows out. How many lead shots were dropped into the hemisphere?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1600.

Volume of water flown out = n × Volume of each spherical ball

⇒ 25×23×π×(15)3=n×43×π×0.753\frac{2}{5} \times \frac{2}{3} \times \pi \times (15)^3 = n \times \frac{4}{3} \times \pi \times 0.75^3

⇒ n = 15×15×155×0.75×0.75×0.75\frac{15 \times 15 \times 15}{5 \times 0.75 \times 0.75 \times 0.75}

⇒ n = 1600