Pyramid practice problems - page 3 of 13
A pyramid is a three-dimensional geometric shape with a polygonal base and triangular faces that meet at a common point called the apex (or vertex). The base can be any polygon (e.g., triangle, square, pentagon), and the shape of the pyramid is often named after its base. For example:- A triangular pyramid has a triangular base.
- A square pyramid has a square base.
- A pentagonal pyramid has a pentagonal base.
Key Features of a Pyramid:
1. Base: The polygonal face at the bottom.
2. Faces: The triangular sides connecting the base to the apex.
3. Apex: The topmost point where all the triangular faces meet.
4. Edges: The lines where two faces meet.
5. Height (h): The perpendicular distance from the base to the apex.
Formulas for a Pyramid:
1. Volume (V):
V = 1/3 × Base Area × Height
The volume is one-third of the product of the base area and the height.
2. Surface Area (SA):
Lateral Surface Area (LSA): The sum of the areas of the triangular faces.
Total Surface Area (TSA): The sum of the lateral surface area and the base area.
Number of problems found: 256
- Deviation 4905
The flower bed has the shape of a regular 4-sided pyramid. The edge of the lower plinth is 10 m, and the upper plinth is 9 m. The deviation of the side wall from the base is 45 degrees. How many plantings should be purchased if 90 are needed to plant 1 sq - Six-sided 44151
The parasol has the shape of the shell of a regular six-sided pyramid, whose base edge is a=6dm and height v=25cm. How much fabric is needed to make a parasol if we count 10% for joints and waste? - Dimensions 39623
In the form of a pyramid with a square floor plan, the house's roof has dimensions of 12 x 12 m, at the highest point, a height of 2 m. How much roofing do we need to buy? Count on a 10% reserve. - Tetrahedral pyramid 8
Let all the side edges of the tetrahedral pyramid ABCDV be equally long and its base let us be a rectangle. Find its volume if you know the deviations A=40° B=70° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h=
- Four-sided 27601
The house's roof has the shape of a regular four-sided pyramid 4 m high with a base edge of 100 dm. We consider 30% of the roofing in addition to the overlap. Calculate how much m² of roofing is needed to cover the roof. - 9-gon pyramid
Calculate a nine-sided pyramid's volume and surface, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm. - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - The bus stop
The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how much m² roofing is required to cover the sheathing of three walls, taking 40% of the additional coverage. - Rotatable tower
The rotatable tower situated in the city center has the ground shape of a regular polygon. If the tower is rotated by 18° around its centerpiece, it looks from the side same. Your task is to calculate at least how many vertices can have a ground plan view
- House roof
The house's roof is a regular quadrangular pyramid with a base edge 17 m. If the roof pitch is 57° and we calculate 11% of waste, connections, and overlapping of the area roof, how much m² is needed to cover the roof? - Dimensions 44081
In the form of a pyramid on the house with a square floor plan, the roof has dimensions of 12 x 12 m, with a height of 2 m at the highest point. How much roofing do I need to buy? Count on a 10% reserve. - The roof The house's roof has the shape of a regular quadrilateral pyramid 5 m high and the edge of the base 7 m. How many tiles with an area of 540 cm² are needed?
- Triangular pyramid
A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.
- Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid with a height equal to the base edge, which is 10 cm long. - Pyramid roof
1/3 of the area of the roof-shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still need to be covered? - Nine-sided 36071
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm - Quadrilateral 30401
Calculate the volume of a regular quadrilateral pyramid, given: 1) a = 3.5 m; vt = 24 dm Express the volume in m³ and round to 1 decimal place 2) a = 1.6 dm; vt = 295 mm Calculate the volume in cm³ and round to 1 decimal place Solution entry: 1) entry 2) - Base diagonal In a regular four-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the pyramid's surface area and volume.
The tent has the shape of a regular square pyramid. The edge of the base is 3 m long, and the tent's height is 2 m. Calculate how much cover (without a floor) is used to make a tent.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
