# 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:

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

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. Water tank
What is the height of the cuboid-shaped tank with the bottom dimensions of 80 cm and 50 cm if the 480 liters of water reaches 10 cm below the top?
Find the radius of the circle with area S = 200 cm².
3. Rectangle 45
The perimeter of a rectangle is 60cm. If the length of the rectangle is 20cm. a)find the width b)find the area.
4. The schoolyard
The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m2 and has a square shape again. How many meters was each side of the yard enlarged?
5. A plasticine
Jožko modeled from plasticine. He used 27g of plasticine to model a 3 cm long cube. How many grams of plasticine will it need to mold cubes with an edge of 6cm?
6. A cylindrical tank
A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
7. Edges or sides
Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
8. The perimeter 3
The perimeter of a rectangle is 35 cm. The ratio of the length to its width is 3:2. Calculate the dimensions of the rectangle
9. Quotient
Find quotient before the bracket - the largest divisor 51 a + 34 b + 68 121y-99z-33
10. Sum of four numbers
The sum of four consecutive natural numbers is 114. Find them.
11. Two thirds
Find two-thirds of the number equal to two-thirds of 99
12. A number 2
A number decreased by the difference between four and the number
13. An equilateral triangle
The perimeter of an equilateral triangle is 33cm. How long is each side?