Pyramid practice problems - page 11 of 14

Number of problems found: 262

Equilateral tetrahedral pyramid
The base edge of a regular tetrahedral pyramid is a = 4 cm. The base and walls are equilateral. Calculate the surface of this pyramid.
Tetrahedron
What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
Rectangular base
Calculate the pyramid's surface area with a rectangular base measuring 9cm, 4cm, and 6cm high.
Tetrahedron - surface
Calculate the surface area of a regular tetrahedron whose height is 9 cm.
Rectangular base - II
Calculate the volume of a pyramid with a rectangular base with sides a = 7 cm, b = 5 cm, and height of the pyramid v = 13 cm.
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
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?
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.
The projection
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.
Octagonal pyramid
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.
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 92 cm² and 207 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
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.
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.
Quadrilateral 46431
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 = 27m³

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