Uboid volume

Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²

Correct answer:

V =  210 cm³

Step-by-step explanation:

$$\begin{gathered} S_1=ab=30 \\ {S}_2=bc=35 \\ {S}_3=ac=42 \\ V=abc \\ {S}_1\cdot S_2\cdot S_3=ab\cdot bc\cdot ac=a^2\cdot b^2\cdot c^2 \\ {S}_1\cdot S_2\cdot S_3=(abc{)}^2=V^2 \\ V=\sqrt{S_1\cdot S_2\cdot S_3} \\ V=\sqrt{30\cdot 35\cdot 42}=210{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Cuboid walls
  Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm².
• Quadrangular prism
  Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
• Cuboid walls
  If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?
• Pebble
  The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
• Cube walls
  Find the volume and surface area of the cube if the area of one wall is 40cm².
• 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?
• 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 the surface of the prism?
• Rectangle 35
  Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
• 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.
• Hexagonal prism 2
  The regular hexagonal prism has a surface of 140 cm² and height of 5 cm. Calculate its volume.
• Body diagonal
  The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
• Cuboid and eq2
  Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm².
• 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.
• Regular square prism
  The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
• Block or cuboid
  The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
• Trapezoid
  Area of trapezoid is 135 cm². Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...