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The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height of
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1 m 3
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2 m 3
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2√2 m 3
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4 m 3
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Correct Option: D
Given R = 1, radins of sphere.
Let height of cone is H = h + R
| Volume , V = | π × (√R² - h²)2(R + h) | |
| 3 |
for maximum value ,
| ⇒ | = 0 | |
| dh |
| ⇒ |  | (R² - h²)(R + h) |  | ||
| dh | 3 |
⇒ -2h(R + h) + (R² - h²) = 0
⇒ (R + h)(R - 3h) = 0
| h = -R , | ||
| 3 |
| Height of the come = R + | = | ||
| 3 | 3 |
| = | m = | m | ||
| 3 | 3 |
