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SSC MTS 2024 PYQ — Question 10

SSC MTS - 08/10/2024 - (12:30 PM - 2:30 PM) • Quantitative Aptitude • Q10

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A solid cone of base radius 7 cm and height 18 cm is melted and recast into a hollow metal hemisphere of internal and external radii 20 cm and R cm, respectively. What is the value of R (in cm)?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 84413\sqrt[3]{8441}.

Volume of solid cone = 13πr2h\frac{1}{3} \pi r^2 h

⇒ 13×227×72×18\frac{1}{3} \times \frac{22}{7} \times 7^2 \times 18 = 924 cm3

Volume of hollow hemisphere = 23π(R3−203)\frac{2}{3} \pi (R^3 - 20^3)

⇒ 23π(R3−8000)\frac{2}{3} \pi (R^3 - 8000) = 924

⇒ (R3 - 8000) = 924×32π\frac{924 \times 3}{2 \pi}

⇒ (R3 - 8000) = 27722×227\frac{2772}{2 \times \frac{22}{7}} = 2772×744\frac{2772 \times 7}{44} = 441

⇒ R3 = 8441

⇒ R = 84413\sqrt[3]{8441}