# Axial section

Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.

Result

V =  136.5 cm3

#### Solution:

$S = \pi \cdot \dfrac{a}{2}(\dfrac{a}{2}+a) = \dfrac{3}{4}\pi a^2 = 168 \ cm^2 \ \\ a = \sqrt{ \dfrac{4S}{3\pi}} = 8.44 \ cm \ \\ h = \sqrt {a^2-\dfrac{a^2}{2}} = 7.31 \ cm \ \\ \ \\ V = \dfrac{1}{3} \pi r^2 h = 136.5 \ cm^3$

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...):

Be the first to comment!

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Rotation
The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
2. Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
3. Truncated cone 5
The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
4. Cone 15
The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
5. Cone area and side
Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
6. Pyramid roof
2/4 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
7. Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
8. 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.
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?