To find the dimensions of the largest cylinder that can be inscribed in a sphere, one needs to relate the cylinder's radius and height to the sphere's radius using geometric constraints (Pythagorean theorem on a cross-section) and then maximize the cylinder's volume formula by treating it as a function of one variable.
The height of the cylinder of maximum volume that can be inscribed in a sphere of radius 'a' is - - $(1) \frac{\sqrt{2}}{3}a$ - $(2) \frac{2a}{3}$ - $(3) \frac{\sqrt{2a}}{3}$ - $(4) \frac{2a}{\sqrt{3}}$ - (5) Question not attempted
Asked in Asst. Statistical Officer (Agri. Deptt.) 2024 · Topic: Mechanics (Lagrangian Formulation (Generalized Coordinates, Euler-Lagrange Equations))
More Physics questions
- The radius of curvature of $y^2 = 2x (3- x^2)$ at the points where the tangents are parallel to x-axis is - - (1) $\frac{1}{2}$ - (2) $ \frac{1}{4}$ - (3) $\frac{1}{5}$ - (4) $\frac{1} {3}$ - (5) Question not attempted
- A cuboid has six sides of different colours. The red side is opposite to black. The blue side is adjacent to white. The brown side is adjacent to blue. The red side is face down. Which one of the following would be opposite to brown?
- Running at a speed of 60 km per hour, a train passes through a 1.5 km long tunnel in two minutes. What is the length of the train?
- A washing machine works on the principle of
- A man can row 7 1/2 km per hour in still water. If in a river running at 1 1/2 km an hour, it takes him 50 minutes to row to a place and back, how far off is the place?
- A train of length 150 meters, moving towards north direction at a speed of 144 km/hr, can cross a 250 meters long bridge in
- If x² - y² = 7 and x - y = 1, then the length of a diagonal of a rectangle with length and width respectively x cm and y cm will be
- Which one of the following is a scalar quantity?