Diagonal - math word problems - page 22 of 28
Number of problems found: 546
- 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° - Three faces of a cuboid
The diagonals of the three walls of a cuboid are 13, √281, and 20 units long, respectively. Thus, the cuboid's total surface area is. - Diamond base
The prism with a diamond base has 24 cm and 20 cm long base diagonals. Calculate the height of a prism with a volume of 9.6 dm³ (cubic decimetres) - Prism
Calculate the volume of the rhombic prism. The prism base is a rhombus whose one diagonal is 47 cm, and the edge of the base is 27 cm. The edge length and height of the base of the prism are 4:3. - Axial section
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - Quadrilateral prism
A regular quadrilateral prism ABCDEFGH has a base edge A B 8 cm long and 6 cm high. Point M is the center of the edge AE. Determine the distance of point M from the BDH plane. - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Quadrilateral pyramid
In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the base's diagonal is 50 cm. Calculate the pyramid shell area. - Cube measurements
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double that of one of the square bases. What is the length of the body diagonal? - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - Calculate diagonals
Calculate the length of the solid diagonals of a prism with a rhombus base if the sizes of the base diagonals are 16 cm and 20 cm and the height of the prism is 32 cm. Calculate the size of the base edge. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Cube diagonals
Determine the length of the body and wall diagonals of the cube, the volume of which is equal to 0.343 decimetres. Also, calculate its surface. - Cube triangle volume
In the cube ABCDEFGH, the area of triangle ABK is √20 cm². How much cm² is the volume of ABGH in a cube if you know that K is the midpoint of edge CG? - Cylinder helix length
A regular helix is drawn on the shell of the cylinder such that it wraps around the cylinder precisely three times (that is, the point where it touches the upper base is exactly above the point where it touches the lower base). If the diameter of the cyli - Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. - Pyramid edge calculation
We know a regular quadrilateral pyramid's base diagonal length of u = 4 cm. The height of the pyramid is v = 5cm. Calculate the size of the side edge and the base edge of the pyramid. - Prism 4 sides
The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism (BG) is 5 cm. Calculate the surface of this prism in cm square and the volume in liters. - Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
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