{"id":92924,"date":"2025-06-01T11:36:53","date_gmt":"2025-06-01T11:36:53","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92924"},"modified":"2025-06-01T11:36:53","modified_gmt":"2025-06-01T11:36:53","slug":"a-solid-metal-ball-of-diameter-10-cm-is-melted-and-cast-into-smaller-b","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metal-ball-of-diameter-10-cm-is-melted-and-cast-into-smaller-b\/","title":{"rendered":"A solid metal ball of diameter 10 cm is melted and cast into smaller b"},"content":{"rendered":"

A solid metal ball of diameter 10 cm is melted and cast into smaller balls of diameter 1 cm. How many such small balls can be made ?<\/p>\n

[amp_mcq option1=”250″ option2=”500″ option3=”1000″ option4=”100″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\n1000 small balls can be made from the solid metal ball.
\n<\/section>\n
\nWhen a solid is melted and recast into smaller solids, the total volume remains constant (assuming no loss of material). The number of smaller solids is the ratio of the volume of the larger solid to the volume of a single smaller solid.
\n<\/section>\n
\nThe volume of a sphere is given by the formula $V = \\frac{4}{3}\\pi r^3$, where $r$ is the radius.
\nThe large ball has a diameter of 10 cm, so its radius is $R = 10\/2 = 5$ cm.
\nThe volume of the large ball is $V_{large} = \\frac{4}{3}\\pi (5^3) = \\frac{4}{3}\\pi \\times 125$ cm\u00b3.
\nEach smaller ball has a diameter of 1 cm, so its radius is $r = 1\/2 = 0.5$ cm.
\nThe volume of a small ball is $V_{small} = \\frac{4}{3}\\pi (0.5^3) = \\frac{4}{3}\\pi \\times (1\/8)$ cm\u00b3.
\nThe number of small balls, N, is the total volume of the large ball divided by the volume of a single small ball:
\n$N = \\frac{V_{large}}{V_{small}} = \\frac{\\frac{4}{3}\\pi \\times 125}{\\frac{4}{3}\\pi \\times (1\/8)} = \\frac{125}{1\/8} = 125 \\times 8$.
\n$125 \\times 8 = 1000$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A solid metal ball of diameter 10 cm is melted and cast into smaller balls of diameter 1 cm. How many such small balls can be made ? [amp_mcq option1=”250″ option2=”500″ option3=”1000″ option4=”100″ correct=”option3″] This question was previously asked in UPSC CISF-AC-EXE – 2021 Download PDFAttempt Online 1000 small balls can be made from the … <\/p>\n

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