Circle practice problems - page 38 of 50
Number of problems found: 990
- Motion on circle
The bend has a radius of r = 100 m and is inclined at an angle of 20° to the horizontal plane (= tilt angle). What is the safe (the "best") speed to go through this curve? Sketch the picture regarding NIVS, mark the forces, and calculate. - The cap
A rotating cone shapes a jester hat. Calculate how much paper is needed for the cap 53 cm high when the head circumference is 45 cm. - Calculate cylinder
In the rotating cylinder, it is given: V = 120 cm3, v = 4 cm. Calculate r, S mantle. - Elevation
What must be an observer's elevation so that he may see an object on the Earth 866 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km. - Cone-shaped 44161
How many square meters of roofing is needed to cover the cone-shaped roof if the perimeter of its base is 15.7m and a height of 30dm - Triangular prism
The curved part of the rotating cylinder is four times larger than the area of its base. Determine the volume of the regular triangular prism inscribed in the cylinder. The radius of the bottom of the cylinder is 10 cm. - A plane vs. sphere
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere. - Draw triangle
Construct right triangle MNO with hypotenuse o = 5 cm and angle MNO = 37° - Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv, and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane. - Horizon
The top of a lighthouse is 18 m above the sea. How far away is an object just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.] - Square inscribed
Find the length of the side of the square ABCD, which is inscribed to a circle k with a radius of 10 cm. - Hexagon, hexa S, V
What is the surface area and volume of a regular hexagonal prism with a base edge of 12cm and a height of the prism equal to the diameter of the circle circumscribed by the base? - Dodecagon
Find the area of a regular dodecagon (n=12) if the radius of the circumscribed circle is 5 cm. - Same area
There is a given triangle. Construct a square of the same area. - Round flowerbed
I will make a sidewalk up to 0.5 meters wide around a round flowerbed with a diameter of 6 meters. How much gravel is needed if the layer is 5 cm high? - Sphere cuts
At what distance from the center does the sphere intersect with the radius R = 46 plane if the cut area and area of the main sphere circle are in ratio 2/5? - 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? - Masquerade ball
Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? The hat side length is 30cm. Add 5% of the material to the bust. Round to cm². - Two chords
In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle. - Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
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