Diagonal of Square Problems - page 14 of 18
Number of problems found: 355
- Angle of diagonal
The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10 cm. Calculate the body volume. - Cylinder surface
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Longest rod
The toolbox has internal dimensions, a length of 1.5 meters, a width of 80 cm, and a height of 6 dm. Calculate the longest rod we can hide in this box. - Two balls
Two balls, one 8 cm in radius and the other 6 cm in radius, are placed in a cylindrical plastic container 10 cm in radius. Find the volume of water necessary to cover them. - Box volume
Calculate the volume of a wooden box in the shape of a prism with the base of a rectangle if the box's width is 8 dm, the length is 14 dm, and the size of the body diagonal is 25 dm. - Axial section
The axial section of the cylinder has a diagonal 50 cm. The shell size and base surface are in the ratio 2:5. Calculate the volume and surface area of this cylinder. - Suitcase - rod
The boot of a car has the shape of a cuboid with dimensions 1.6 m × 1.2 m × 0.5 m (width × depth × height). Determine the longest thin rod that can be placed flat on the bottom of the boot. - 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. - Prism Box Force Weight
We turn the prism-shaped box with a height of 1 m and a square base with an edge of 0.6 m under a force of 350 N, which acts horizontally compared to the upper edge. What is the weight of the box? - Trunk
Calculate the length of the longest fishing rod that can be placed in a car boot with dimensions 152 × 82 × 81 cm. - Cylinder volume diagonal
The axial section of the cylinder is a rectangle with a diagonal of u = 20 cm. The height of the cylinder is twice the diameter of the base. Calculate the cylinder volume in liters. - Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - 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. - Cuboid's diagonal
The cuboid has a body diagonal u=25 cm, and side b is one-third longer than side a. What is the volume of the cuboid? - Sphere cube filling
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill? - 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. - 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? - Pyramid volume calculation
Calculate the volume of a regular quadrilateral pyramid, which has the size of the base edge a = 8 cm and the length of the side edge h = 9 cm. - Cube measurements
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals.
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