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.


S1 =  86.535 cm2
S2 =  34.614 cm2
S3 =  43.267 cm2


V=360 a:b:c=5:4:2 V=abc=5 4 2 k3 k=V/(5 4 2)3=360/(5 4 2)32.0801 a=5 k=5 2.080110.4004 b=4 k=4 2.08018.3203 c=2 k=2 2.08014.1602 S1=a b=10.4004 8.320386.53586.535 cm2V=360 \ \\ a:b:c=5:4:2 \ \\ V=abc=5 \cdot \ 4 \cdot \ 2 \cdot \ k^3 \ \\ k=\sqrt[3]{ V/(5 \cdot \ 4 \cdot \ 2)}=\sqrt[3]{ 360/(5 \cdot \ 4 \cdot \ 2)} \doteq 2.0801 \ \\ a=5 \cdot \ k=5 \cdot \ 2.0801 \doteq 10.4004 \ \\ b=4 \cdot \ k=4 \cdot \ 2.0801 \doteq 8.3203 \ \\ c=2 \cdot \ k=2 \cdot \ 2.0801 \doteq 4.1602 \ \\ S_{1}=a \cdot \ b=10.4004 \cdot \ 8.3203 \doteq 86.535 \doteq 86.535 \ \text{cm}^2
S2=b c=8.3203 4.160234.61434.614 cm2S_{2}=b \cdot \ c=8.3203 \cdot \ 4.1602 \doteq 34.614 \doteq 34.614 \ \text{cm}^2
S3=c a=4.1602 10.400443.267543.267 cm2S_{3}=c \cdot \ a=4.1602 \cdot \ 10.4004 \doteq 43.2675 \doteq 43.267 \ \text{cm}^2

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.



Next similar math problems:

  1. 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.
  2. Scale factor
    cuboid_7 A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
  3. 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
  4. 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?
  5. Cube corners
    polyhedra-truncated-cube From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
  6. Cross-sections of a cone
    kuzel_rezy Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
  7. The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  8. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  9. Gas consumption
    vessel The vessel consume 100 tons of gas in 250 miles. How many fuel will the vessel consume if it travels 400 miles?
  10. The edge of a cube
    cubes How much does the edge of a cube of 54.9 cm3 measure?
  11. Bottles
    flasa_1 The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
  12. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  13. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  14. Numbers at ratio
    number-2_2 The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?
  15. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  16. Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8
  17. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4