A solid metallic sphere of radius 6.3 cm is melted and recast into cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1 : 2
| Understanding | Application |
| Tricks |
The volume of the Sphere = 4/3πr3 = 4/3 × 22/7 × 6.3 6.3 6.3 = 1047.816 |
| Now |
The volume of the cone = 1/3 πr2h ⇒ 1047.816 = 1/3 × 22/7 × r2 × 25.2 ⇒ 1047.816 = 554.4/21 × r2 ⇒ 1.89 × 21 = r2 ⇒ 39.69 = r2 ⇒ r = 6.3 So d = 12.6 |
| Hence |
Ratio = 12.6/25.2 = 1/2 |