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SSC Selection Post 2020 PYQ — Question 58

SSC Selection Post - Graduation Level 2020 - 14 Dec 2020 - Shift 3 • Quantitative Aptitude • Q58

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Find the number of lead balls, each with a diameter of 3 cm, that can be made from a sphere of diameter 21 cm.

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 343.

Volume of bigger sphere = 43πR3{4\over3}\pi R^3

⇒ 43×π×212×212×212{4\over3}\times{\pi}\times {21\over2}\times {21\over2}\times {21\over2}

Volume of lead balls = 43πr3{4\over3}\pi r^3

⇒ 43×π×32×32×32{4\over3}\times{\pi}\times {3\over2}\times {3\over2}\times {3\over2} 

Number of lead balls(n) =  Volume of bigger sphere/Volume of lead balls

⇒ n = 43×π×212×212×21243×π×32×32×32{4\over3}\times{\pi}\times {21\over2}\times {21\over2}\times {21\over2} \over{4\over3}\times{\pi}\times {3\over2}\times {3\over2}\times {3\over2}

⇒ n = 9261279261\over27 = 343