Pyramid - high school - practice problems - page 5 of 6
Number of problems found: 107
- Regular quadrilateral pyramid
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm. - Quadrilateral 5277
Given a regular quadrilateral pyramid ABCDV, point M is inside its edge AV, and point N is on the long line DC beyond point C. Construct the intersection of the plane MNV with the plane BCV and the intersection of the line MN and the plane BCV. - Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long?
- Tetrahedron
Calculate the height and volume of a regular tetrahedron whose edge has a length of 13 cm. - 4s pyramid
A regular tetrahedral pyramid has a base edge a=17 and a collateral edge length b=32. What is its height? - Tetrahedron
What is the angle of the sides from the base of a three-sided pyramid where the sides are identical? - Rectangular 46201
Calculate the pyramid's surface with a rectangular base measuring 9cm and 4cm, and 6cm high. - Tetrahedron 5844
Calculate the surface area of a regular tetrahedron whose height is 9 cm.
- Perpendicular 3494
In axonometry, construct the projection of a perpendicular 4-sided pyramid with a square base ABCD in the plane. The base triangle gives the axonometry. We know the center of the base S, the point of the base A, and the height of the pyramid v. - Right pyramid
A right pyramid on a base 4 cm square has a slanted edge of 6 cm. Calculate the volume of the pyramid. - Mystery of stereometrie
Two regular tetrahedrons have surfaces 76 cm² and 171 cm². In what ratio are their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - 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.
- 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. - 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. - Pit
The pit has the shape of a truncated pyramid with a rectangular base and is 0.8 m deep. The pit's length and width are the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of the pit, we use 0.6 l of green color. How many liters of paint are ne - 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? - Flowerbed
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 plante
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Pyramid practice problems. Examples for secondary school students.