Pyramid practice problems - page 12 of 14
Number of problems found: 262
- Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - Quadrilateral 46431
Calculate the volume V and the surface S of a regular quadrilateral pyramid, the base edge and height of which are the same size as the edge of a cube with a volume V1 = 27m3 - Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - Ice cream maker
Ice cream maker Eda has invented a new nice cone in the shape of a regular four-sided pyramid, in which he will sell his ice cream. The cone will have a side edge length of 5 cm and a wall height of 4 cm. In order to mass-produce it in the factory, they s - In a regular 5
In a regular triangular prism ABCV, the deviation of the side wall and the base plane is α = 45°. Determine the deviation of the side edge and the base plane. - Calculate - prism
The base of the prism is a square with a side of 10 cm. Its height is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume. - Pyramid 7903
How does the volume of a pyramid change if we triple its height?
- Tower
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer, there were six cubes (in one row) in six rows. In each subsequent layer, always one cube and one row less. What volume in cm³ did the whole tower have? - Calculate 25321 Calculate the body's volume, consisting of a prism and a pyramid with the same square base with an edge of 8 cm. The prism is 20 cm high, and the pyramid is 15 cm.
- Consumption 15663
The cone-shaped sheet metal roof has a base diameter of 80 cm and a height of 60 cm. If 1 kg of paint is consumed per 6 m² of sheet metal, calculate the paint consumption for painting this roof. - Consumption 4259
What is the consumption of fabric per tent: Length 250, width 180, the height of triangle 120, sides 150 (all cm). What is the volume of air in the tent? - From plasticine
Michael modeled from plasticine a 15 cm high pyramid with a rectangular base, with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter of 10 cm. How tall was Janka's cone? - Pit
The pit is 1.2 m deep and in the shape of a truncated pyramid with a rectangular base. Its length and width are the top 3 × 1.5 m and the bottom 1 m × 0.5 m. To paint one square meter of the pit, we use 0.8 l of green paint. How many liters of paint are n - Cone
The rotating cone volume is 9.42 cm3, with a height of 10 cm. What angle is between the side of the cone and its base? - Rotating cone
How does the volume of the rotating cone change if: a) double the radius of the base b) We reduce the height three times c) Reduce the radius of the base five times
- Calculate 83248
The cube ABCDEFGH has an edge of length 3 cm. Calculate the volume of the pyramid ABCDH. - Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot? - Flowerbed
The flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be pl - Tetrahedron 82497
The sum of the lengths of all the edges of the regular tetrahedron ABCD is 48 cm. How many cm is the segment XY if you know that X is AB's midpoint and Y is CD's midpoint? - Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.
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