Space diagonal + right triangle - practice problems - page 2 of 5
Number of problems found: 91
- 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 10cm. Calculate the body volume. - Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Diagonals 5551
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Cube wall
Calculate the cube's diagonal if you know that one wall's surface equals 36 centimeters square. Please also calculate its volume. - Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonally. - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - Dimensions 6264
Calculate the length of the body diagonal of a block whose dimensions are a = 5cm, b = 6cm, c = 10cm.
- 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 - Block-shaped 39241
The boys wanted to store their hand-made totem 5.1 m high in the block-shaped shed, which measures 4 m, 3 m, and 2 m, for the winter. Will it fit in there at all? - Calculate 32133
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals. - Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Dimensions 4700
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. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Identical 35961
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? - Dimensions - crate
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si
- Body diagonal
Calculate the volume of a cuboid whose body diagonal u equals 6.1 cm. The rectangular base has dimensions of 3.2 cm and 2.4 cm. - Nice prism
Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Calculate 6214
The cube A B C D A'B'C'D 'has a section area ACC'A' equal to 64 square root of 2 cm². Calculate the surface of the cube. - 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?
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