# Tetrahedral prism

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.

Result

a =  9 cm

#### Solution:

$a^2 h = 2187 \ \\ a^2 3a = 2187 \ \\ a^3 = 729 \ \\ a = \sqrt[3]{729} = 9 \ \text { cm } \ \\$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

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

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

1. Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the larges
2. 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?
3. Cylinder - area
The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
4. Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
5. Balls
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
6. Cube
The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
7. Sphere growth
How many times grow volume of sphere if diameter rises 10×?
8. Tereza
The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
9. Sphere
The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
10. Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
11. Cube zoom
How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
12. Lathe
From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
13. Hollow sphere
Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm3), if the inner diameter is 14 cm and wall thickness is 3 mm.
14. Cube in ball
Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
15. Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
16. Hollow sphere
Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
17. Plasticine ball
Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls.