Body volume + area of shape - examples
- Regular triangular pyramid
Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
- Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
- Iron density
Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
Annual rainfall in our country are an average of 797 mm. How many m3 of water rains on average per hectare?
- Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
- Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.
- The pot
The pot is in 1/3 filled with water. Bottom of the pot has an area of 329 cm2. How many centimeters rises water level in the pot after add 1.2 liters of water?
Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool?
- Road embankment
Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
- 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.
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.
- 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.
- Hexagonal prism
The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
- Triangular prism
Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
- Children pool
The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film.
- Tetrahedral prism
Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.