# Cuboid + expression of a variable from the formula - math problems

A cuboid is a three-dimensional shape with a length, width, and a height. A cuboid is a rectangular Prism. The cuboid shape has six sides called faces. Each face of a cuboid is a rectangle, and all of a cuboid's corners (called vertices) are 90-degree angles. Opposite faces are parallel. A cuboid has the shape of a rectangular box.

1. 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.
2. Body diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
3. Faces diagonals If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
4. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
5. Prism X The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
6. Nice prism Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
7. 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.
8. Aquarium 6 How high is the water level in the aquarium with a rectangular base 40cm and 50cm if it is filled 0,65hl of water?
9. Cuboid - volume and areas The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
10. Water in aquarium The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water.
11. Cuboid walls Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
12. Square vs rectangle Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
13. Floor Rectangular floor of living room has a length 5.4 meters and a circumference 17.2 meters. What is its width?
14. Third dimension Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
15. Body diagonal Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
16. Prism Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
17. Cuboid and eq2 Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.
18. Cuboid - edges The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
19. Cuboid and ratio Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
20. Cuboid - ratios The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm2. Calculate the surface area and volume of this cuboid.

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