Pyramid practice problems - page 12 of 14

Number of problems found: 267

Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has an area of 10 cm². Find the area of the or
Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
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.
Pyramid
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
In a regular 5
In a regular triangular prism ABCV, the angle between the lateral face and the base plane is α = 45°. Determine the angle between the lateral edge and the base plane.
Pyramid volume surface
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 = 27 m³
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.
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?
Prism pyramid volume
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.
Ice cream maker
Ice cream maker Eda has invented a new cone in the shape of a regular four-sided pyramid, in which he will sell his ice cream. The cone will have a lateral edge length of 5 cm and a slant height of 4 cm. In order to mass-produce it in a factory, the dimen
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 volume change
How does the volume of a pyramid change if we triple its height?
Tent fabric
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?
Roof paint consumption
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.
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
Gravel - cone
The mound of gravel has a regular circular cone shape with a height of 3.3 meters and a base circumference of 18.85 meters. How many cubic meters of gravel are in a pile? Calculate the weight of gravel if its density is p = 640 kg/cubic m.
Cube pyramid volume
The cube ABCDEFGH has an edge of length 3 cm. Calculate the volume of the pyramid ABCDH.
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, Jane modeled a rotating cone with a base diameter of 10 cm. How tall was Jane's cone?
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?
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

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