find the volume of the largest circular cone that can fit in a sphere of radius 3 cm.
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Expert's answer
2012-08-21T10:53:35-0400
The volume of a right circular cone is V = 1/3 π r2 h. To apply the calculus you know you need to express this volume as a function of one variable. The right triangle ABC give the information you need.
Let R = radius sphere r = base radius cone R + h = height cone V = volume cone _______
V = (1/3)πr²(R + h)
By the Pythagorean Theorem: r² = R² - h²
Plug into the formula for volume. V = (1/3)π(R² - h²)(R + h) = (1/3)π(R³ + R²h - Rh² - h³)
Take the derivative and set equal to zero to find the critical points.
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