Cuboid - ratios

The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm2. Calculate the surface area and volume of this cuboid.


S =  558 cm2
V =  810 cm3


a=2x b=3x c=5x ab=54 6x2=54 x=54/6=3 a=2 x=2 3=6 b=3 x=3 3=9 c=5 x=5 3=15 S1=a b=6 9=54 S2=b c=9 15=135 S3=a c=6 15=90 S=2 (S1+S2+S3)=2 (54+135+90)=558 cm2a=2x \ \\ b=3x \ \\ c=5x \ \\ ab=54 \ \\ 6x^2=54 \ \\ x=\sqrt{ 54/6 }=3 \ \\ a=2 \cdot \ x=2 \cdot \ 3=6 \ \\ b=3 \cdot \ x=3 \cdot \ 3=9 \ \\ c=5 \cdot \ x=5 \cdot \ 3=15 \ \\ S_{1}=a \cdot \ b=6 \cdot \ 9=54 \ \\ S_{2}=b \cdot \ c=9 \cdot \ 15=135 \ \\ S_{3}=a \cdot \ c=6 \cdot \ 15=90 \ \\ S=2 \cdot \ (S_{1}+S_{2}+S_{3})=2 \cdot \ (54+135+90)=558 \ \text{cm}^2
V=a b c=6 9 15=810 cm3V=a \cdot \ b \cdot \ c=6 \cdot \ 9 \cdot \ 15=810 \ \text{cm}^3

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
Looking for help with calculating roots of a quadratic equation?
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

  1. Volume of three cuboids
    image10 Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.
  2. Carpenter
    tesari From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
  3. Cuboid and ratio
    kvader Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
  4. Cuboid - edges
    kvadr The sum of all edges cuboid are 8 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid.
  5. Juice box 2
    pfanner-ananas Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of th
  6. Cuboid enlargement
    cubes_12 By how many percent increases the volume of cuboid if its every dimension increases by 30%?
  7. Volume increase
    basen_6 How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
  8. Digging
    Dighole A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ?
  9. Swimming pool
    basen The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
  10. 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?
  11. Gasoline tank cylindrical
    cisterna What is the inner diameter of the tank, which is 8 m long and contains 40 cubic cubic meters of gasoline?
  12. Book read
    books_12 If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?
  13. Donuts
    donut Find how many donuts each student will receive if you share 126 donuts in a ratio of 1:5:8
  14. Liters od milk
    milk_cylinder The cylinder-shaped container contains 80 liters of milk. Milk level is 45 cm. How much milk will in the container, if level raise to height 72 cm?
  15. 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?
  16. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  17. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)