Cuboid - examples
- Water block
A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
- 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%?
A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
The swimming pool is 4 m wide and 20 m long and 156 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
- Transforming cuboid
Cuboid with dimensions 5 cm, 14 and 17 cm is converted into a cube with the same volume. What is its edge length?
In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
Fire tank has cuboid shape with a rectangular floor measuring 14.5 m × 9.8 m. Water depth is 2 m. Water was pumped from the tank into barrels with a capacity of 3 hl. How many barrels were used, if the water level in the tank fallen 12 cm? Write
Annual rainfall in our country are an average of 854 mm. How many m3 of water rains on average per hectare?
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
Gift box has rectangular shape with dimensions of 4×9×19 cm. Todd wants to cover with square paper with sides of 27 cm. How much paper left him?
Brick has volume 2.2 dm3. How many bricks can drive truck with capacity 20 ton? The density of brick is 2 g/cm3.
Determine the dimensions of the cuboid, if diagonal long 16 dm has angle with one edge 66° and with other edge 71°.
- Air mass
What is the weight of the air in a classroom with dimensions 5 m × 2 m × 3.1 m ? The air density is 1.293 kg/m3.
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. What is the area of surface of the prism?
- The pot
The pot is in 1/5 filled with water. Bottom of the pot has an area of 193 cm2. How many centimeters rises water level in the pot after add 2.2 liters of water?
Three cubes are glued into prism, sum of the lengths of all its edges is 259 cm. What is the length of one edge of the original cube?
Room is 26.2 m long, 23.4 dm wide and 628 cm high. How many people can simultaneously be in this room if for hygiene reasons is calculated 5100 dm3 of air per person?
Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60°