Angle + cylinder - practice problems
Number of problems found: 9
- Rotational motion of a cylinder
Calculate the kinetic energy of a cylindrical body with radius r = 0.08 m and mass m = 1.5 kg at time t = 5 s, given that the body rotates about an axis through the centre of the cylinder with a constant angular acceleration ε = 5 rad/s², starting from re - Right-angled trapezoid
A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is: - Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Find the ratio of surfaces of the first and second bo - A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly six complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - Hexagon rotation
A regular hexagon of side 6 cm is rotated at 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2 m. How many hectoliters of water can fit into the pool? - Total displacement
Calculate the total displacement of the 12-cylinder engine with the diameter of the piston bore B = 8.9 cm and stroke S=1.9 cm of the piston. Help: The crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and b - Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling.
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