Diagonal - math word problems - page 21 of 28
Number of problems found: 553
- Cuboid
A cuboid with edge a = 6 cm and space diagonal u = 31 cm has a volume of V = 900 cm³. Calculate the lengths of the other two edges. - Axial section
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm². Calculate the radius of the base. - Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - 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. - Diamond base
A prism with a rhombus-shaped base has base diagonals of 24 cm and 20 cm. Calculate the height of the prism if its volume is 9.6 dm³. - 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? - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Cuboid
Find the dimensions a, b, and c of a cuboid whose space diagonal is d = 6 dm and makes an angle α = 35° with edge a and an angle β = 66° with edge b. - 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 - Ratio-cuboid
The edges of a cuboid are in the ratio 2:3:6. Its space diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - 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.
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