# Regular triangular pyramid

Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters

Result

V =  96 cm3
S =  96 cm2

#### Solution:

$h = 12 \ cm \ \\ a = 4 \ cm \ \\ h_{ 2 } = 12 \ cm \ \\ \ \\ S_{ 1 } = a \cdot \ h_{ 2 }/2 = 4 \cdot \ 12/2 = 24 \ cm^2 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 24 \cdot \ 12 = 96 = 96 \ cm^3$
$S = 4 \cdot \ S_{ 1 } = 4 \cdot \ 24 = 96 = 96 \ cm^2$

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...):

Be the first to comment!

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.

## Next similar math problems:

1. Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
2. Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
3. Cheops pyramid
The Pyramid of Cheops is a pyramid with a square base with a side of 233 m and a height of 146.6 m. It made from limestone with a density of 2.7 g/cm3. Calculate the amount of stone in tons. How many trains with 30 twenty tons wagons carry the stone?
4. A square base
A solid right pyramid has a square base. The length of the base edge is 4 centimeters and the height of the pyramid is 3 centimeters. What is the volume of the pyramid?
5. Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
6. Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
7. Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
8. A concrete pedestal
A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
9. Length of the edge
Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
10. Cylinder
The 1.8m cylinder contains 2000 liters of water. What area (in dm2) of this container is the water?
11. Frustum of a cone
A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
12. Two cylinders
Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are p
13. 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?
14. Swimming pool
The swimming pool has the shape of a block with dimensions of 70dm, 25m, 200cm. How many hl of water can fit into the pool?
15. A filter
It is a pool with a volume of 3500 liters. The filter filters at 4m cubic per hour. How many minutes would it filter the entire pool?
16. The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
17. Floating of wood - Archimedes law
What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m3 and a volume of 0.02 m3 that floats in alcohol? (alcohol density is 789 kg/m3)