# 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:

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

1. Two rectangular boxes Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
2. Free space in the garden The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
4. Cuboid and ratio 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
5. An example An example is playfully for grade 6 from Math and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: A cuboid was made from a block of 16x18x48 mm of modeline. What will be the edge of
6. Triangular prism, The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l).
7. Tropics and polar zones What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'
8. Squares ratio The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
9. Water container The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
10. The edge of a cube How much does the edge of a cube of 54.9 cm3 measure?
11. Wall thickness The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
12. Profitable company Three businessman decide to open up their own company. They agree to distribute the yearly profits made in the same ratio as their initial investments. They invest R 50 000, R 75 000 and R25 000, respectively. The profit made by the company in the first y
13. Power line pole From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
14. Tetrahedral pyramid 8 Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p
15. Volume of wood Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
16. Growth of wood The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
17. Mortage hypo loan The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?