Pythagorean theorem + cylinder - practice problems - last page
Number of problems found: 31
- Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - 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. - Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which we cut the spherical cap.
- 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 - 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? - 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. - 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.
- 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. - Turning machine
What is the smallest diameter of the cylinder so that a square prism with a side of 40 cm can be turned from it?
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