Space diagonal - practice problems - page 3 of 6
Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.Number of problems found: 114
- Block measurements
Calculate the solid diagonal of a block whose dimensions are: a = 3cm, b = 5, c = 7cm. Find its volume as well. - 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? - 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. - Cuboidal room
The length of the cuboidal room is 2m the breadth of the cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room - 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-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. - Trunk
Calculate the length of the biggest fishing rod that can be inserted into the trunk of a car with dimensions 152 x 82 × 81 cm. - Whistle fit
Peter wants to hide a 60 cm long whistle in a shoebox that measures 25 cm x 48 cm x 21 cm. Will he make it? - 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? - Cube measurements
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double that of one of the square bases. What is the length of the body diagonal? - Cube diagonals
If you know the length of the body diagonal u = 216 cm, determine the cube's volume and surface area. - 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? - Cube triangle volume
In the cube ABCDEFGH, the area of triangle ABK is √20 cm². How much cm² is the volume of ABGH in a cube if you know that K is the midpoint of edge CG? - 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. - Block diagonal length
Calculate the length of the body diagonal of a block measuring 6 cm, 7 cm, and 10 cm, and round the result to two decimal places. - Cube dimension calculation
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals. - Cube from Body Diagonal
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Cube wall
Calculate the cube's diagonal if you know that one wall's surface equals 36 centimeters square. Please also calculate its volume.
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