Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?

Correct result:

S =  4950 cm2

Solution:

V=20250 cm3  V=abc=x⋅ 2x⋅ 3x=6x3 x=V63=2025063=15 cm a=x=15 cm b=2⋅ x=2⋅ 15=30 cm c=3⋅ x=3⋅ 15=45 cm S=2⋅ (a⋅ b+b⋅ c+a⋅ c)=2⋅ (15⋅ 30+30⋅ 45+15⋅ 45)=4950 cm2V=20250 \ \text{cm}^3 \ \\ \ \\ V=abc=x \cdot \ 2x \cdot \ 3x=6x^3 \ \\ x=\sqrt[3]{ \dfrac{ V }{ 6 } }=\sqrt[3]{ \dfrac{ 20250 }{ 6 } }=15 \ \text{cm} \ \\ a=x=15 \ \text{cm} \ \\ b=2 \cdot \ x=2 \cdot \ 15=30 \ \text{cm} \ \\ c=3 \cdot \ x=3 \cdot \ 15=45 \ \text{cm} \ \\ S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (15 \cdot \ 30+30 \cdot \ 45+15 \cdot \ 45)=4950 \ \text{cm}^2

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:
#
Savage Math Hacker 21
i think that all math is great but cubes graphic is better.????????

#
Dr Math
graphics fixed

avatar






Tips to related online calculators
Do you want to convert length units?

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Cuboid edges in ratio
    cuboid_11 Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
  • Tetrahedral prism
    hranol_1 The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm3.
  • Balls
    steel_ball Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
  • Cuboid height
    kvader11_8 What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
  • 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.
  • Sphere A2V
    sphere3 Surface of the sphere is 241 mm2. What is its volume?
  • Cylinder - A&V
    cylinder The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
  • Sphere growth
    sphere How many times grow volume of sphere if diameter rises 10×?
  • Square roots
    roots What is equal to the product of the square roots of 295936?
  • Cylinder
    cylinder The cylinder surface is 922 dm2, its height is equal to the radius of the base. Calculate height of this cylinder.
  • Power
    power Number ?. Find the value of x.
  • One half
    one_half One half of ? is: ?
  • Powers
    1power Express the expression ? as the n-th power of the base 10.
  • 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?
  • Calculation
    pocty How much is sum of square root of six and the square root of 225?
  • Root
    sq_root Use law of square roots roots: ?
  • Quotient
    fun1_1 Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.