# Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.

Result

V =  144.338 cm3
S =  193.364 cm2

#### Solution:

$a = 10 \ cm \ \\ h = a = 10 = 10 \ cm \ \\ \ \\ S_{ 1 } = \dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2 = \dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 10^2 = 25 \ \sqrt{ 3 } \ cm^2 \doteq 43.3013 \ cm^2 \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 43.3013 \cdot \ 10 \doteq 144.3376 = 144.338 \ cm^3$
$r = \dfrac{ \sqrt{ 3 } }{ 6 } \doteq 0.2887 \ cm \ \\ h = \sqrt{ h^2+r^2 } = \sqrt{ 10.0042^2+0.2887^2 } \doteq 10.0042 \ cm \ \\ S_{ 2 } = \dfrac{ 1 }{ 2 } \cdot \ a \cdot \ h = \dfrac{ 1 }{ 2 } \cdot \ 10 \cdot \ 10.0042 \doteq 50.0208 \ cm^2 \ \\ \ \\ S = S_{ 1 } + 3 \cdot \ S_{ 2 } = 43.3013 + 3 \cdot \ 50.0208 \doteq 193.3638 = 193.364 \ cm^2$

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 1 comment:
Reynie
Easy problem solving????????????????????????

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

Tip: Our volume units converter will help you with the conversion of volume units. Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

## Next similar math problems:

1. 4side pyramid
Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
2. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
3. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
4. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
5. Pyramid a+h
Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
6. Axial section
Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
7. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
8. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
9. Cone
Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
10. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
11. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
12. Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
13. Cuboid
Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.