Cylinder + Pythagorean theorem - practice problems
Number of problems found: 31
- 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? - The glass
The glass has the shape of a cylinder with an inner diameter of 12 cm, and the height from the bottom is 16 cm. The cut skewer can be inserted diagonally into the glass so it does not protrude beyond the edge. What is the largest possible length of the cu - Tank
In the middle of a cylindrical tank with a bottom diameter of 251 cm is a standing rod that is 13 cm above the water surface. If we bank the rod, its end reaches the water's surface just by the tank wall. How deep is the tank? - Calculate 5115
In the rotating cylinder, it is given: V = 120 cm3, v = 4 cm. Calculate r, S mantle. - Calculate 74024
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - Calculate 70634
The axial section of the cylinder is a rectangle with a diagonal of u = 20 cm. The height of the cylinder is twice the diameter of the base. Calculate the cylinder volume in liters. - Calculate 4842
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Axial section
The axial section of the cylinder has a diagonal 36 cm long, and we know that the area of the side and the base area is in ratio 1:1. Calculate the height and radius of the cylinder base. - Floating barrel
The barrel (cylinder shape) floats on water, the top of the barrel is 8 dm above water, and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Precisely 82088
A regular helix is drawn on the shell of the cylinder such that it wraps around the cylinder precisely three times (that is, the point where it touches the upper base is exactly above the point where it touches the lower base). If the diameter of the cyli - Cross-section 4343
Premium quality olive oil is sold in a glass bottle with a square cross-section packed in a special cylinder tube. The square's perimeter that forms the bottle's cross-section is 28 cm. What is the radius of this tube? - Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Axial section
The axial section of the cylinder has a diagonal 40 cm. The shell size and base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - A paint
A paint tin is a cylinder of 12cm and a height of 22 cm. Leonardo, the painter, drops his stirring stick into the tin, and it disappears. Work out the maximum length of the stick. - Cylinder-shaped 4410
A cylinder-shaped case is to be made for a ruler with the shape of a prism with a base in the shape of an equilateral triangle with a side length of 3 cm. What must be the smallest inner diameter of the housing? Determine the size to the nearest tenth of - Triangular 6610
The shell of the rotating cylinder is four times larger than the contents 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. - Container 15093
A cone-shaped container with a bottom diameter of 60 cm and a side length of 0.5 m is filled with water. We pour the water into a container with the face of a cylinder with a radius of 3dm and a height of 20cm. Will the cylinder overflow or not be complet - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Surrounded 8283
The cube has an edge length of 5 cm. This cube surrounds a rotating cylinder. Find the surface area of the shell and the volume of the cylinder.
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