Pyramid practice problems
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 = 13 × 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: 262
- Januka
Januka and her father were going to the tent. They found that their old tent was torn. Their mother suggested that they sew a tent whose walls would be made of 4 identical isosceles triangles. Their lower side is 2 m long, and the height is also 2 m. Then - A cone 3
A cone has a diameter of x cm and a slant height of y cm. A square pyramid has a base side length of x cm and a slant height of y cm. Which has the greater surface area? Explain. - Storage shed
Frank designed a net for a storage shed that he is going to construct out of metal. The design consists of a square base and four square sides, plus four triangular parts that make up the roof. A square base of 6 feet and four square sides, plus 4 feet of - A frustum
A frustum of a pyramid consists of a square base of length 10 cm and a top square of length 7 cm. The height of the frustum is 6 cm. Calculate the surface area and volume. - The frustum A frustum of a pyramid is 4 cm at the top and 7 cm at the bottom square, and it's 6 cm high. Calculate the volume of the frustum.
- Census pyramid
Vojta added five different prime numbers to the top row of the census pyramid. Their sum was 50. What was the biggest number he could get "down"? - Metal pyramid
Find the weight of a regular quadrilateral pyramid with a 5 cm length and 6,5 cm body height made from material with density g/cm³.
- Chocholate pyramid
How many chocolates are on the third shelf when on the 8th shelf are 41 chocolates on any other shelf? Are seven chocolates more than the previous shelf? - Pyramid Z8–I–6
Each brick of the pyramid contains one number. Whenever possible, the number in each brick is the lowest common multiple of two numbers of bricks lying directly above it. May that number be in the lowest brick? Determine all possibilities. - Tableau pyramid
Your class will invent an original tableau pyramid from photos. What minimum dimensions will it have to have if you want to place 50 9x13 photos there? You want a classic pyramid, i.e., Each next row is one photo-less, but in the last row, two photos (the - Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm. - Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m. The pyramid height is 1.6 m. How many square meters of sheet metal are needed to cover the top of the tower if 15% extra sheet metal is needed for join - Sun rays
If the sun's rays are at an angle of 60°, then the famous Great Pyramid of Egypt (which is now 137.3 meters high) has a 79.3 m long shadow. Calculate the current height of the neighboring Chephren pyramid, whose shadow is measured at the same time at 78.8 - Quadrilateral pyramid
Calculate the volume of a regular quadrilateral pyramid, which has the size of the base edge a = 12 cm and a height of 11 cm. - The roof
The tower's roof has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste.
- Isosceles triangle
Jan and her father were going to the tent. They found that their old tent was torn. Their mother suggested that they sew a tent with walls comprising six identical isosceles triangles. Their lower side is 2 m long, and the height to this side measures 2.5 - Quadrilateral 22003
The shelter has the shape of a regular quadrilateral pyramid without a front wall. The length of the base edge is 3 meters, and the shelter's height is 3.5 meters. How much canvas must be bought to sew it if we have to increase consumption by 20% for fold - Four-sided 5917
Mr. Radomír had a misfortune during the last storm; a tree fell on his roof in the shape of a regular four-sided pyramid and destroyed it all. The roof has a base edge length of 8m and a side edge length of 15m. How many m² of roofing will he have to buy? - The tent
The tent shape of a regular quadrilateral pyramid has a base edge length of a = 2 m and a height of v = 1.8 m. If we have to add 7% of the seams, how many m² of cloth did we need to make the tent? How many m³ of air will be in the tent? - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place.
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