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CUET General Test 2023 PYQs5 June Shift 2. Free, no login required.

Geometry

past year questions, CUET General Test 2023 5 June Shift 2

Solids

past year questions, Geometry, CUET General Test 2023 5 June Shift 2

Medium

A solid metallic sphere of radius 8 cm is melted and recasted as a cone of height 8 cm. Find the base radius of the cone (in cm).

Solution

✅ Correct Option: 3

Volume is conserved. Volume of sphere =43πR3=43π(8)3= \frac{4}{3}\pi R^3 = \frac{4}{3}\pi(8)^3. Volume of cone =13πr2h=13πr2(8)= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi r^2 (8). Equating: 43π×512=8πr23\frac{4}{3}\pi \times 512 = \frac{8\pi r^2}{3}, so r2=256r^2 = 256, giving r=16r = 16 cm.

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