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SSC CGL 2025 PYQ — Question 60

SSC CGL - 15 Sep 2025 - Shift 2 • Quantitative Aptitude • Q60

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A right circular cone has raidus of 7 cm and a height of 24 cm. A sphere is palced inside the cone wuch that it touches the base and the slanted surface of the cone. Find the radius of this inscribed sphere. 

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 5.25 cm.

For cone:

Radius R = 7 cm

Height h = 24 cm

Slant height(l) = 72+242\sqrt{7^2 + 24^2}

⇒ 49+576\sqrt{49 + 576} = √625 = 25 cm

Radius of sphere inscribed in cone(r) = (R×h)(R+l)(R × h)\over(R + l)

⇒ 7×247+257 × 24 \over 7 + 25 = 16832168 \over 32 = 5.25 cm