Rectangular cuboid

The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.

Result

V =  23519.015 cm3

Solution:

a=2 x b=4 x c=5 x S=5334 cm2  S=2(ab+bc+ac)=2(2⋅ 4 x2+4⋅ 5 x2+2⋅ 5 x2) S=76 x2  x=S/76=5334/76≐8.3776 cm  a=2⋅ x=2⋅ 8.3776≐16.7552 cm b=4⋅ x=4⋅ 8.3776≐33.5104 cm c=5⋅ x=5⋅ 8.3776≐41.888 cm  V=a⋅ b⋅ c=16.7552⋅ 33.5104⋅ 41.888≐23519.0145≐23519.015 cm3a=2 \ x \ \\ b=4 \ x \ \\ c=5 \ x \ \\ S=5334 \ \text{cm}^2 \ \\ \ \\ S=2(ab+bc+ac)=2(2 \cdot \ 4 \ x^2 + 4 \cdot \ 5 \ x^2 + 2 \cdot \ 5 \ x^2) \ \\ S=76 \ x^2 \ \\ \ \\ x=\sqrt{ S / 76 }=\sqrt{ 5334 / 76 } \doteq 8.3776 \ \text{cm} \ \\ \ \\ a=2 \cdot \ x=2 \cdot \ 8.3776 \doteq 16.7552 \ \text{cm} \ \\ b=4 \cdot \ x=4 \cdot \ 8.3776 \doteq 33.5104 \ \text{cm} \ \\ c=5 \cdot \ x=5 \cdot \ 8.3776 \doteq 41.888 \ \text{cm} \ \\ \ \\ V=a \cdot \ b \cdot \ c=16.7552 \cdot \ 33.5104 \cdot \ 41.888 \doteq 23519.0145 \doteq 23519.015 \ \text{cm}^3

Try another example


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 2 comments:
#
Amy
Not very useful plz give worked example with steps

2 years ago  2 Likes
#
Dr Math
Example is complete with solution  step-by-step

avatar









Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Check out our ratio calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Surface of cuboid
    kvader11_9 Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
  2. Cuboid - simple
    cuboid_6 Calculate the surface area and volume of a cuboid if a = 8 cm, b = 14 cm and c = 6 cm.
  3. Cuboid
    cuboid_12 Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
  4. Third dimension
    star_1 Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
  5. Peppers
    paprika In the box are yellow (a), green (b) and red (c) peppers. Their amount is in a ratio 2:4:1 . Most are yellow peppers and green the least. Calculate the number of peppers each type if the total number of peppers is 70.
  6. Guppies
    guppies Audrey has some guppies in a fish tank. The ration of the oranges guppies to silver guppies is 3:5. She has 12y oranges guppies. Write the number of silver guppies she has in terms of y
  7. Two machines
    machine_2 Performances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift. a) How many pieces produced per shift second machine? b) How many pieces produced two machines together for five shifts?
  8. Unknown number 24
    numbs_6 f we add 20, we get 50% of its triple. What is this unknown number?
  9. Quiz
    quiz Tested student answered correctly on a 4/ 8 questions. Wrong answers was 16. How many questions answered?
  10. A number
    number_line_4 A number increased by 7.9 is 8.3
  11. Strange x
    pie For what x is true ??
  12. Equation 11
    rovnice Solve equation: ?
  13. Powers
    math_fun Is true for any number a,b,c equality:? ?
  14. Simple equation 8
    eq1 Solve the following equation: 36=-(1+7x)-6(-7-x)
  15. Equation 29
    eq222_18 Solve next equation: 2 ( 2x + 3 ) = 8 ( 1 - x) -5 ( x -2 )
  16. Simple equation 10
    eq1_1 35= 7*3*x what is x?
  17. Unknown number
    nums Identify unknown number which 1/5 is 40 greater than one tenth of that number.