Pyramid practice problems - page 11 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
- 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 pyramid's volume. - Quadrilateral 82052
Calculate the volume of a regular quadrilateral pyramid with a square base of side a=8 cm and a height of the pyramid of 11 cm.
- Quadrilateral 35053
Calculate the volume of a regular quadrilateral pyramid, the base edge of which measures 6 cm and the height 10 cm - Quadrilateral pyramid
Calculate the volume of a quadrilateral pyramid, the base of which has the shape of a rectangle with dimensions a = 6cm, b = 4cm, and height v = 11cm - Projection 4514
Draw an octagonal pyramid in free parallel projection if the length of the edge a = 3 cm and the height of the pyramid v = 6 cm. - Regular triangular pyramid
Calculate the volume and surface area of the regular triangular pyramid. The height of the pyramid is 12 centimeters. The bottom edge is 4 centimeters, and the height of the sidewall is 12 centimeters. - A square base
A solid right pyramid has a square base. The base edge length is 4 centimeters, and the pyramid's height is 3 centimeters. What is the volume of the pyramid?
- Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m. - Perpendicular 82488 For the volumes of a perpendicular prism and a pyramid with the same base and height: A) the volumes are equal B) the volume of a pyramid is three times smaller than the volume of a prism C) the ratio of the volumes of the prism and the pyramid is 1:3 D)
- Special body
Above each wall of a cube with an edge a = 30 cm, we construct a regular quadrilateral pyramid with a height of 15 cm. Find the volume of the resulting body. - 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. - Approximately 44981
The largest Egyptian pyramid has the shape of a regular four-sided pyramid with a base edge of approximately 227 meters and a height of about 140 meters. How many tons of stone did the workers transport to build it? One cube of stone weighs 2500 kg and ne
- 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 - 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. - 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
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - 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.
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.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
