Solid geometry, stereometrySolid geometry is the name for the geometry of three-dimensional Euclidean space.
Stereometry involves the measurements of volumes of various solid figures (three-dimensional figures), including pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.
Number of problems found: 1105
- Transforming cuboid
Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
The water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flows the same speed?
Calculate the length of the biggest fishing rod that can be inserted into the trunk of a car with dimensions 165 x 99 × 85 cm?
Observatory dome has the shape of a hemisphere with a diameter d = 20 m. Calculate the surface.
- Rotating cone
Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm.
Calculate the angle between box base 9 x 14 and body diagonal length 18.
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
- Gold wire
From one gram of gold was pulled wire 2.1 km length. What is its diameter if the density of Au is ρ=19.5 g/cm3?
Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
- Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
- Conserving water
Calculate how many euros are spent annually on unnecessary domestic hot water, which cools during the night in pipeline. Residential house has 129 m of hot water pipelines 5/8" and the hot water has a price of 7 Eur/m3.
- Sphere cuts
At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
- Sphere slices
Calculate the volume and surface of a sphere if the radii of parallel cut r1=31 cm, r2=92 cm, and its distance v=25 cm.
- Lead cube
Calculate the edge of the cube made from lead, which weighs 19 kg. The density of lead is 11341 kg/m3.
- Cone and cube
About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r?
- Truncated cone
Calculate the volume of a truncated cone with base radiuses r1=13 cm, r2 = 10 cm and height v = 8 cm.
Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
- Copper sheet
The copper plate has a length of 1 m, width 94 cm and weighs 9 kg. What is the plate thickness, if 1 m3 weighs 8715 kg?
Calculate the dimensions of rotating cylindrical containers with volume 2 l if the container's height is equal to the base's diameter.
- Glass of juice
Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
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