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.

Result

V =  1521.69 cm3
S =  774.566 cm2

Solution:

h=10 cm r=8 cm n=5  a=2 r sin(π/n)=2 8 sin(3.1416/5)9.4046 cm h1=r2(a/2)2=82(9.4046/2)26.4721 cm  S1=n a h12=5 9.4046 6.47212152.169 cm2  V=S1 h=152.169 101521.69041521.69 cm3h=10 \ \text{cm} \ \\ r=8 \ \text{cm} \ \\ n=5 \ \\ \ \\ a=2 \cdot \ r \cdot \ \sin(\pi/n)=2 \cdot \ 8 \cdot \ \sin(3.1416/5) \doteq 9.4046 \ \text{cm} \ \\ h_{1}=\sqrt{ r^2-(a/2)^2 }=\sqrt{ 8^2-(9.4046/2)^2 } \doteq 6.4721 \ \text{cm} \ \\ \ \\ S_{1}=n \cdot \ \dfrac{ a \cdot \ h_{1} }{ 2 }=5 \cdot \ \dfrac{ 9.4046 \cdot \ 6.4721 }{ 2 } \doteq 152.169 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=152.169 \cdot \ 10 \doteq 1521.6904 \doteq 1521.69 \ \text{cm}^3
S=2 S1+n a h=2 152.169+5 9.4046 10774.5663774.566 cm2S=2 \cdot \ S_{1} + n \cdot \ a \cdot \ h=2 \cdot \ 152.169 + 5 \cdot \ 9.4046 \cdot \ 10 \doteq 774.5663 \doteq 774.566 \ \text{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 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

 

 

 

Next similar math problems:

  1. Square prism
    lichob_2 Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
  2. Hexa pyramid
    hexa_pyramid_1 The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
  3. Triangular prism
    prism3 Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm.
  4. Regular n-gon
    10gon_polygon In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
  5. The cylinder 2
    cylinder Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
  6. Concentric circles
    medzikruzie2 There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
  7. Inscribed circle
    vpisana The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
  8. Rain
    bowl-water How many mm of water rained the roof space 75 m2 if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-)
  9. The cylinder base
    valec_4 The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
  10. Roller
    cestnyvalec Roller has a diameter of 0.96 m and a width 169 cm. How many m2 of road level when he turns 42-times?
  11. Disc
    vysek.JPG Circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc?
  12. Juice box 2
    pfanner-ananas Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of th
  13. Trapezium
    trapezium_1 The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
  14. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  15. Cone area and side
    cone_2 Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
  16. Cube volume
    cube6 The cube has a surface of 384 cm2. Calculate its volume.
  17. Cube 1-2-3
    cube_shield_1 Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.