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 result:

S =  4950 cm2

Solution:

V=20250 cm3  V=abc=x⋅ 2x⋅ 3x=6x3 x=V63=2025063=15 cm a=x=15=15 cm b=2⋅ x=2⋅ 15=30 cm c=3⋅ x=3⋅ 15=45 cm S=2⋅ (a⋅ b+b⋅ c+a⋅ c)=2⋅ (15⋅ 30+30⋅ 45+15⋅ 45)=4950 cm2

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 2 comments:
#
Savage Math Hacker 21
i think that all math is great but cubes graphic is better.????????

#
Dr Math
graphics fixed

avatar









Tips to related online calculators
Do you want to convert length units?
Tip: Our volume units converter will help you with the conversion of volume units.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Cuboid edges in ratio
    cuboid_11 Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
  • Magnified cube
    cube_in_sphere If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
  • Surface of cubes
    cubes3_6 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?
  • Uboid volume
    cuboid Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
  • Cube surface and volume
    cube_diagonals_5 The surface of the cube is 500 cm2, how much cm3 will be its volume?
  • Cube 1-2-3
    cube_shield_1 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.
  • Triangular prism
    prism3_1 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?
  • Three cubes
    cubes3 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 and ratio
    cuboid_2 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
  • Minimum surface
    cuboid_20 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.
  • Prism bases
    hranoly 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
    cubes_20 Volume of the cube is 216 cm3, calculate its surface area.
  • Two boxes-cubes
    3-kostky 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?
  • Balls
    steel_ball Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
  • Volume and area
    cubes_8 What is the volume of a cube which has area of 361 cm2?
  • Rhombus base
    paral_prism Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 15 cm. Prism height is twice base edge length.
  • Body diagonal
    kvader11_1 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?