Geometry - math word problems - page 159 of 163
Number of problems found: 3251
- Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base. - Deviation - slope angle
Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30° from the base plane. - Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees). - Cuboid
Find the dimensions of cuboids a, b, and c; if diagonal d=6 dm has an angle with edge α=35° and has an angle with edge b β=66° - 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. - Deviation of the lines
Find the deviation of the lines AG BH in the ABCDEFGH box-cuboid if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees. - Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went? - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - 9-sided pyramid
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 - Horizontal watertank
We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. Calculate how many liters of water is in first centimeters. - Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal. - Pyramid - angles
In a regular pyramid in which the edge of the base is | AB | = 4 cm; height = 6 cm, calculate the angle of the lines AV and CV, V = vertex. - Quadrilateral prism
The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body. - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=16 cm and the side of the cone with the base has angle 37°12'. - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm, and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Calculate cone
The rotating cone has a base radius r = 226 mm, and the deviation of the side from the base plane is 56°. Calculate the height of the cone. - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - 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
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