Solid geometry, stereometry - page 19Solid 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.
Mr Peter has metal roof cone shape with a height of 101 cm and radius 189 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 4.3 m2?
- Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
- 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.
- Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
- 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
The base of the prism is a rhombus with a side 30 cm and height 27 cm. The height of the prism is 180% longer than the side length of the rhombus. Calculate the volume of the prism.
- Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
Column with posters in the form of a cylinder is 2.4 m high and its diameter is 2.5 m. What is the content area for which it is possible to stick posters?
Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
- Cylinder - h
Cylinder volume is 163 cm3. Base radius is 10 cm. Calculate the height of the cylinder.
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
- House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1111 cm3 and a base radii r1 = 6.2 cm and r2 = 9.8 cm.
- Pentagonal pyramid
Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
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 ar
- Cardboard box
We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal
- Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
- Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
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