Container

The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?

Correct result:

x =  65 cm

Solution:

$$\begin{gathered} a=3.9\text{ m}\to \text{ cm}=3.9\cdot 100\text{ cm}=390\text{ cm } \\ b=3.25\text{ m}\to \text{ cm}=3.25\cdot 100\text{ cm}=325\text{ cm } \\ c=2.6\text{ m}\to \text{ cm}=2.6\cdot 100\text{ cm}=260\text{ cm } \\ 390=2\cdot 3\cdot 5\cdot 13 \\ 325=5^2\cdot 13 \\ 260=2^2\cdot 5\cdot 13 \\ \text{GCD}(390,325,260)=5\cdot 13=65 \\ x=GCD(a,b,c)=GCD(390,325,260)=65\text{ cm} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar 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.
• Two boxes-cubes
  Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its 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.
• Cremons
  The freight wagon is shaped like cuboid 21m and 3.5m and 4.2m How many cremons can be loaded if one is a cube with an edge length of 7 cm?
• Water pool
  What water level is in the pool shaped cuboid with bottom dimensions of 25 m and 10 meters, when is 3750hl water in the pool.
• Identical cubes
  From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?
• Wooden container
  The cube-shaped wooden container should be covered with a metal sheet inside. The outer edge of the container is 54cm. The wall thickness is 25 mm. The container has no lid. Calculate. How many sheets will be needed to cover it?
• Aquarium
  The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edg
• Wood prisms
  How many weight 25 prisms with dimensions 8x8x200 cm? 1 cubic meter of wood weighs 800 kg.
• Flowerpot
  The block-shaped flowerpot has external dimensions: length 1.25 m, width 10 cm and height 11 cm. The thickness of the boards from which it is made is 0.8 cm. How many liters of soil is needed to fill it 1 cm below the top edge? What surface do we have to
• 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?
• Tetrapack
  How high should be the milk box in the shape of a prism with base dimensions 8 cm and 8.8 cm if its volume is 1 liter?
• Wooden box
  The block-shaped box was placed on the ground, leaving a rectangular print with dimensions of 3 m and 2 m. When flipped over to another wall, a print with dimensions of 0.5 m and 3 m remained in the sand. What is the volume of the wooden box?
• Tank
  To cuboid tank whose bottom has dimensions of 9 m and 15 m were flow 1080 hectoliters of water. This was filled 40% of the tank volume. Calculate the depth of the tank.
• Balls
  Ping pong balls have a diameter of approximately 5.1 cm. They are sold in boxes of 10 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w
• Flower boxes
  How many m² of 10mm thick boards are needed to make 12 flower boxes? The dimensions of the box are 180,150 and 1500 mm.
• Transforming cuboid
  Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?