# Cuboid + diagonal - practice problems

#### Number of problems found: 46

- Volume and body diagonal

Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%? - Trunk

Calculate the length of the biggest fishing rod that can be inserted into the trunk of a car with dimensions 165 x 99 × 85 cm? - Cardboard box

We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca - Faces diagonals

If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Side wall planes

Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - 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°. - 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. - Deviation of the lines

Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - 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. - Cuboid face diagonals

The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be 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. - Right triangular prism

We have a cuboid with a base and dimensions of 12 cm and 5 cm and a height of 4 cm. The tablecloth is cut into two identical triangular prisms with right triangular bases. We painted the surface of the created prisms with color. Calculate the surface area - Body diagonal

The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Diagonals of a prism

The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base. - 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. - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Ratio-cuboid

The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism. - 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. - 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. - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N, and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}, and F_{3}.

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Cuboid practice problems. Diagonal - practice problems.