SpletNow by pythagorus theorem ((h-r)^2)+(R^2)=(r^2). Now express R in terms of h and r. We get (R^2)=(2hr-hh). Substitute in the volume of cone equation V=(pi/3)(R^2)h. Now V=(pi/3)(2hr-hh)h. Differentiate wrt h with r as … Splet09. okt. 2024 · Max volume occurs when d V d x = 0 Then 2 3 π ⋅ r 2 x ⋅ r 2 − ( r x) 2 = 1 3 π ( r x) 2 ⋅ − r 2 x r 2 − ( r x) 2 Which reduces to 2 r 2 = 3 ( r x) 2 And x = 2 3 Therefore the ratio …
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Splet20. avg. 2024 · Given a right circular cylinder which is inscribed in a cone of height h and base radius r. The task is to find the largest possible volume of the cylinder. Examples: Input: r = 4, h = 8 Output: 119.087 Input: r = 5, h = … Splet10. jan. 2024 · To calculate the volume of a cone, follow these instructions: Find the cone's base area a. If unknown, determine the cone's base radius r. Find the cone's height h. … footter css
What is the largest cone you can fold from a circular sector?
Splet3. Select the quantity which is to be made a maximum or minimum and express it as a function of the other quantities. 4, Use information in the problem fo eliminate all quantities but one so os to have a function of one variable. 5. differentiate and equate to zero, to get ‘the maximum or minimum. Splet07. avg. 2024 · Input: R = 10 Output: Volume of cone = 8373.33 Explanation: Radius of cone = 14.14 and Height of cone = 40, Volume of cone = So, volume = 8373.33 Input: R = 4 Output: Volume of cone = 535.89. Approach: we have given a sphere of radius R inscribed in Cone. We need to find out the radius and height of the cone to find out the volume of the … SpletThe volume of the cylinder is hence V = π r 2 h = π ( h R 2 − h 3 4). Differentiating with respect to h and equating to 0 to find extrema gives d V d h = π ( R 2 − 3 h 2 4) = 0 ∴ h 0 = 2 R 3 The second derivative of the volume with respect to h is negative if h > 0 such that the volume is maximal at h = h 0. Substituting gives foot terminal