# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry deals with 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: 956

- 4s pyramid

Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height? - Tetrahedron

Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm. - Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm^{2}and 198 cm^{2}. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1115 cm^{3}and a base radii r_{1}= 7.9 cm and r_{2}= 9.7 cm. - Roller

Roller has a diameter of 0.96 m and a width 169 cm. How many m^{2}of road level when he turns 42-times? - Box

Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm^{2}of cardboard we need to cover overlap and joints that are 5% of are - Prism

The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - Axial section

Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - Spherical segment

Spherical segment with height h=5 has a volume V=117. Calculate the radius of the sphere of which is cut this segment. - Axial section

Axial section of the cone is an equilateral triangle with area 168 cm^{2}. Calculate the volume of the cone. - Plastic pipe

Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m^{3}. - Rotation

The right triangle with legs 11 cm and 18 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - Spherical cap

From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere? - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Cuboid

Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm^{3}. Calculate the length of the other edges. - Canopy

Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m^{2}? - Earth's circumference

Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - Rainfall

Annual rainfall in our country are an average of 797 mm. How many m^{3}of water rains on average per hectare?

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