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?

Correct answer:

S =  4950 cm²

Step-by-step explanation:

$$\begin{gathered} V=20250{\text{cm}}^3 \\ V=abc=x\cdot 2x\cdot 3x=6x^3 \\ x=\sqrt[3]{{\displaystyle \frac{V}{6}}}=\sqrt[3]{{\displaystyle \frac{20250}{6}}}=15\text{ cm } \\ a=x=15\text{ cm } \\ b=2\cdot x=2\cdot 15=30\text{ cm } \\ c=3\cdot x=3\cdot 15=45\text{ cm } \\ S=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (15\cdot 30+30\cdot 45+15\cdot 45)=4950{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 2 comments:

Savage Math Hacker 21

i think that all math is great but cubes graphic is better.????????

3 years ago  Like

Dr Math

graphics fixed

3 years ago  Like

Related math problems and questions:

• 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.
• Balls
  Three metal balls with volumes V₁=71 cm³ V₂=78 cm³ and V₃=64 cm³ melted into one ball. Determine it's surface area.
• Cube 1-2-3
  Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
• 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.
• Surface of cubes
  Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each piece made a cube. In what ratio are the surfaces of these cubes?
• 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.
• 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
• 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.
• 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?
• Cube 6
  Volume of the cube is 216 cm³, calculate its surface area.
• Three cubes
  Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge?
• 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.
• Ratio-cuboid
  The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
• Volume and area
  What is the volume of a cube which has an area of 361 cm²?
• Prism
  Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• 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?