Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees.
Correct answer:
Tips for related online calculators
Check out our ratio calculator.
See also our right triangle calculator.
Do you know the volume and unit volume, and want to convert volume units?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
See also our right triangle calculator.
Do you know the volume and unit volume, and want to convert volume units?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
You need to know the following knowledge to solve this word math problem:
- solid geometry
- cuboid
- space diagonal
- surface area
- planimetrics
- right triangle
- area of a shape
- triangle
- diagonal
- basic functions
- ratio
- goniometry and trigonometry
- tangent
Units of physical quantities:
Grade of the word problem:
Related math problems and questions:
- Indoor aquarium
World's biggest indoor aquarium. In its enormous tank with the capacity represented by the following polynomial V=4x³+43x²+63x The aquarium is rectangular prism shape. Find the following: 1. If the aquarium's height is x, then find the area of the base (B - An architect 2
An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume - Cube edges
The cube has an edge of 4 cm. It has the same volume as a block, the base of which has an area of 32 cm². What height is the block? - Cuboid to cube
A cuboid with dimensions of 9 cm, 6 cm, and 4 cm has the same volume as a cube. Calculate the surface of this cube.
- An example
An example is playfully for grade 6 from Math, and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: The student made a cuboid from a block of 16x18x48 mm of plasticine. What will be th - Cuboid and ratio
A cuboid has a volume of 810 cm³. The lengths of edges from the same vertex are in a ratio of 2:3:5. Find the dimensions of a cuboid. - Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - Minimum surface
Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area, into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm, respectively, can be packed. - Volume and body diagonal
Calculate how much the cuboid's volume and body diagonal decrease if we reduce each of its three edges, a, b, and c, by 18%.
- Cuboid edges in ratio
Cuboid edge lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³. - 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? - Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material. - Cuboids in cube
How many can cuboids with dimensions of 6 cm, 8 cm, and 12 cm fit into a cube with a side of 96 centimeters? - For thinkings
The glass cube dives into the aquarium, which has a length of 25 cm, a width of 20 cm, and a height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge?
- Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has a volume 29478 cm³. What is the area of the surface of the prism? - Paul makes
Paul makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube? - Grain storage
On their farm, Adam's family maintains a storage facility that can hold 19.2 cubic yards (yd3) of grain. Since 1 yard is approximately equal to 0.9144 m, this volume can be converted to m³.