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.

Correct 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=5334/768.3776 cm  a=2 x=2 8.377616.7552 cm b=4 x=4 8.377633.5104 cm c=5 x=5 8.377641.888 cm  V=a b c=16.7552 33.5104 41.888=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=23519.015 \ \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 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.

Next similar math problems:

  • A loan
    exp_growth A loan in the amount of $944 is charged simple interest at an annual rate of 8.1%. How much money is owed 14 months after the loan was made?
  • Find the 11
    fractions14 Find the quotient of 229.12 and 12.32
  • Without 2
    calc_4 Without multipying, tell whether the product 0.644 x 0.25 will be greater than 1 or less than 1? Explane how you know. Then find the product.
  • Average price
    mince_1 Sixth grade went on a trip to Moravia. Each of the 26 pupils paid CZK 320 and the school paid a total of CZK 3,510. What was the average price of a trip per student?
  • The fastest
    ship The fastest boat can reach speeds more than 710% as fast as the Queen Mary 2. How would you express this number as a fraction and as a decimal?
  • Tenths digit
    numbers2 For 10.932, which digit is in the tenths place?
  • Barrel
    vino Barrel of wine is filled by 9/14. What part of the barrel will remain filled when 1/4 of the wine we pour from the barrel?
  • Year 2020
    eq222 The four-digit number divided by 2020 gives a result of 1, **. (Can not be in form 1,*0. ) Write all the options.
  • Adding mixed 3
    mixed_fractions Why does 1 3/4 + 2 9/10 equal 4.65? How do you solve this?
  • Fruits 2
    melon An apple costs 7p and a melon costs seven times more. How much will 6 apples and 2 melons cost
  • The temperature
    teplomer_26 The temperature at 1:00 was 10 F. Between 1:00 and 2:00, the temperature dropped 15F. Between 2:00 and 3:00, the temperature rose 3F. What is the temperature at 3:00?
  • Reduce to lowest terms
    fractions_16 Reduce to lowest terms : 32/124
  • Boats
    ship_7 Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
  • Equivalent expressions
    pizza_10 A coach took his team out for pizza after their last game. There were 14 players, so they had to sit in smaller groups at different tables. Six players sat at one table and got 4 small pizzas to share equally. The other players sat at the different table
  • What is one third
    decimals What is 1/3 as a decimal? Give your answer rounded to 2 decimal places.
  • On the trip
    skola_17 On the trip were more than 55 children, but less than 65 children. Groups of 7 could be formed, but groups of 8 no. How many children were on a trip?
  • Double 5
    numbers2_49 Peter was thinking of a number. Peter doubles it and gets an answer of 8.6. What was the original number?