-
A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is :
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- 25%
- 30%
- 50%
- 75%
- 25%
Correct Option: D
| Volume of sphere = | πr³ | |
| 3 |
| = | π × 9 × 9 × 9 = 972π cu.cm. | |
| 3 |
| Volume of cone = | πR²H | |
| 3 |
| = | π × 9 × 9 × 9 = 243π cu.cm. | |
| 3 |
| ∴ Percentage of wood wasted = | × 100 | |
| 972π |
= 75%
Method 2 :
Quicker Approach
In both cases
∵ r = 9, h = 9cm
| ∴ Volume of sphere = | πr³ | |
| 3 |
| and Volume of cone = | πr³ | |
| 3 |
Wasted wood = πr³
| ∴ Required percentage = | × 100 | ||
| πr³ | |||
| 3 | |||
| = | × 100 = 75% | |
| 4 |
