Expression of a variable from the formula + space diagonal - practice problems
Number of problems found: 50
- Calculate 415
Calculate the cuboid's dimensions if the sum of its edges is 19cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - Calculate 82992
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 . - Calculate 82567
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - One-third 77724
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?
- 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 = 28cm, b = 45cm, and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Cuboid diagonals
The cuboid has dimensions of 15, 20, and 40 cm. Calculate its volume and surface, the length of the body diagonal, and the lengths of all three wall diagonals. - 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. - Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, and the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the prism's volume.
- 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. - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Height of the cuboid
Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal, has a body 13 centimeters long. What is the height of the cuboid? - Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - 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.
- 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. - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³. - Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonally.
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