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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 12.2 Surface Area of a Combination of Solids § 12.4 Summary
A cone of height 12 cm and slant height 13 cm is surmounted on a hemisphere having radius equal to that of cone. The entire height of the solid is
  1. A 17 cm
  2. B 18 cm
  3. C 22 cm
  4. D 23 cm
Previously asked in CBSE board exam
2025 30/5/1 Q15
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer

Radius of cone: $r = \sqrt{l^2 - h^2} = \sqrt{13^2 - 12^2} = \sqrt{169-144} = 5$ cm.

Total height = height of cone + radius of hemisphere = 12 + 5 = 17 cm. → Option A

Explanation

The hemisphere's radius equals the cone's base radius (r = 5 cm). The hemisphere adds its radius (not diameter) to the cone's height, giving 12 + 5 = 17 cm. A common mistake is adding the diameter (10 cm) instead.

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Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.