Decagon prism

A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm³, round to two decimal places.

Correct result:

V =  61.5537 cm³

Solution:

$$\begin{gathered} a=2\text{ cm } \\ h=a=2=2\text{ cm } \\ n=10 \\ S=n\mathrm{/}4\cdot a^2\mathrm{/}\tan (\pi \mathrm{/}n)=10\mathrm{/}4\cdot 2^2\mathrm{/}\tan (3.1416\mathrm{/}10)\doteq 30.7768{\text{cm}}^2 \\ V=S\cdot h=30.7768\cdot 2=61.5537{\text{cm}}^3 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Glass
  How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
• Which
  Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm² (B) 20 cm² (C) 30.78 cm² (D) 31.84 cm² (E) 32.90 cm²
• Pentagonal prism
  The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
• Hexagonal prism
  The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
• Quadrilateral pyramid
  In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
• Truncated pyramid
  Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm and the angle that the side wall with the base is 42 degrees
• Triangular prism
  The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C', has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
• Find the
  Find the content of a regular 12 sided polygon, if its side a = 12 cm.
• Mystery of stereometrie
  Two regular tetrahedrons have surfaces 88 cm² and 198 cm². In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
• Hexa prism
  Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
• Angle of diagonal
  Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
• 3s prism
  It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.
• Prism diagonal
  The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
• Quadrilateral prism
  Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
• Triangular prism
  Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
• Cone
  Calculate volume and surface area of ​​the cone with a diameter of the base d=15 cm and side of the cone with the base has angle 52°.