Cube root + body volume - math problems
- Two rectangular boxes
Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
- The edge of a cube
How much does the edge of a cube of 54.9 cm3 measure?
- Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
- Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
- 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
- Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
- The volume 2
The volume of a cube is 27 cubic meters. Find the height of the cube.
- Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
- Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
- Cube surface and volume
Find the surface of the cube with a volume of 27 dm3.
Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
- 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.
- Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
- Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
- Scale factor
A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
- Tower model
Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-dig
- Rectangle pool
Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
- Prism bases
Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
- Cube 6
Volume of the cube is 216 cm3, calculate its surface area.
- Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm3.