Diagonal - math word problems - page 20 of 28
Number of problems found: 553
- Tetrahedron water level
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - 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. - 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. - 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. - Cylinder and Cuboid Volume
A block with a square base is inserted into a 10-centimeter-high cylinder in such a way that its base is inscribed in the base of the cylinder. The edge of the base of the block measures 4 cm. Both bodies have the same height. Calculate the difference bet - Prism and wall diagonal
The ABCDA'B'C'D' prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC' is 11.4 cm long. Calculate the surface area and volume of the prism. - Trapezoidal prism
Calculate the surface of the quadrilateral prism ABCDA'B'C'D' with the trapezoidal base ABCD. The height of the prism is 12 cm; Trapezoid ABCD has the following dimensions: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diag - 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. - Prism - box
The prism's base is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism. - Regular 4BH
A regular quadrilateral prism has a volume of 864 cm³ and its total surface area is twice the area of its base. Determine the length of its space diagonal. - Calculate cuboid
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - 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 | = 3 cm, | AD | = 2 cm, | AE | = 4 cm - Right triangular prism
We have a cuboid with a base and dimensions of 12 cm and 5 cm and a height of 4 cm. The tablecloth is cut into two identical triangular prisms with right triangular bases. We painted the surface of the created prisms with color. Calculate the surface area - Axial section
The axial section of the cylinder is diagonal 45 cm long, and we know that the area of the side and the base area are in the ratio 6:5. Calculate the height and radius of the cylinder base. - Prism volume calculation
The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism. - Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28 cm, b = 45 cm, and c = 73 cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Cube in a sphere
A cube is inscribed in a sphere with volume 8101 cm³. Determine the edge length of the cube.
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