3rd dimension

The block has a surface of 42 dm² and its dimensions are 3 dm and 2 dm. What is the third dimension?

Correct answer:

c =  3 dm

Step-by-step explanation:

$$\begin{gathered} S=42{\text{cm}}^2 \\ a=3\text{ dm } \\ b=2\text{ dm } \\ S=2(ab+bc+ca) \\ S\mathrm{/}2=ab+bc+ca \\ c=(S\mathrm{/}2-a\cdot b)\mathrm{/}(b+a)=(42\mathrm{/}2-3\cdot 2)\mathrm{/}(2+3)=3\text{ dm} \end{gathered}$$

Try another example

Related math problems and questions:

• Cuboid - ratio
  Find the volume of a block whose dimensions are in the ratio 2: 3: 4 and the surface is 117 dm².
• 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.
• Cuboid and eq2
  Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm².
• Cube walls
  Find the volume and surface area of the cube if the area of one wall is 40cm².
• Cuboid edges
  The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m².
• Surface of the cuboid
  Find the surface of the cuboid if its edges have the dimensions a, 2/3a, 2a
• Sphere A2V
  The surface of the sphere is 241 mm². What is its volume?
• Block or cuboid
  The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
• 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?
• The pool
  The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom?
• Edge of prism
  The regular quadrilateral prism has a surface of 250 dm², its shell has a content of 200 dm². Calculate its leading edge.
• Cuboid - ratios
  The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid.
• Volume and surface
  Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm².
• Cubes
  Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm². Determine the length of the edges of this cubes.
• The cube
  The cube has a surface area of 216 dm². Calculate: a) the content of one wall, b) edge length, c) cube volume.
• Cylinder height
  Calculate the height of the cylinder and its surface is 2500 dm² and the bases have a diameter 5dm.
• Cylinder
  The cylinder surface is 922 dm². Its height is equal to the radius of the base. Calculate the height of this cylinder.