# 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 cm2 and 198 cm2. 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 cm3 and a base radii r1 = 7.9 cm and r2 = 9.7 cm.
• Roller Roller has a diameter of 0.96 m and a width 169 cm. How many m2 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 cm2 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 cm2. 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/m3.
• 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 cm3 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 cm3 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 cm3. 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 m2?
• 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 m3 of water rains on average per hectare?

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