# 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.

Result

V =  349.066 cm3
S =  314.159 cm2

#### Solution:

$h = 10 \ cm \ \\ A = 30 ^\circ \rightarrow rad = 30 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ = 30 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ = 0.5236 \ = π/6 \ \\ \ \\ \tan A = r:h \ \\ \ \\ r = h \cdot \ \tan(A) = 10 \cdot \ \tan(0.5236) \doteq 5.7735 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 5.7735^2 \doteq 104.7198 \ cm^2 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 104.7198 \cdot \ 10 \doteq 349.0659 = 349.066 \ cm^3$
$s = \sqrt{ h^2+r^2 } = \sqrt{ 10^2+5.7735^2 } \doteq 11.547 \ cm \ \\ S_{ 2 } = \pi \cdot \ r \cdot \ s = 3.1416 \cdot \ 5.7735 \cdot \ 11.547 \doteq 209.4395 \ cm^2 \ \\ S = S_{ 1 }+S_{ 2 } = 104.7198+209.4395 \doteq 314.1593 = 314.159 \ cm^2$

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
Check out our ratio calculator.
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. 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.
2. The Indian tent
The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire?
3. Hexagon
Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
4. Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
5. Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
6. Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
8. A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
9. 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´.
10. Regular hexagonal pyramid
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
11. Hexagonal pyramid
Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
12. Three parallels
The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
13. Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
14. The aspect ratio
The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
15. Land boundary
The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
16. Two circles
Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
17. Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?