Top of the tower

The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joints, overlap and waste?

Result

S =  7.074 m2

Solution:

a=1.2 m h=1.6 m n=6  h2=h2+(a/2)2=1.62+(1.2/2)21.7088 m S1=n a h22=6 1.2 1.708826.1517 m2 q=15%=1+15100=1.15  S=q S1=1.15 6.15177.07447.074 m2a=1.2 \ \text{m} \ \\ h=1.6 \ \text{m} \ \\ n=6 \ \\ \ \\ h_{2}=\sqrt{ h^2+(a/2)^2 }=\sqrt{ 1.6^2+(1.2/2)^2 } \doteq 1.7088 \ \text{m} \ \\ S_{1}=n \cdot \ \dfrac{ a \cdot \ h_{2} }{ 2 }=6 \cdot \ \dfrac{ 1.2 \cdot \ 1.7088 }{ 2 } \doteq 6.1517 \ \text{m}^2 \ \\ q=15 \%=1 + \dfrac{ 15 }{ 100 }=1.15 \ \\ \ \\ S=q \cdot \ S_{1}=1.15 \cdot \ 6.1517 \doteq 7.0744 \doteq 7.074 \ \text{m}^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
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Hexagonal pyramid
    hexa_pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
  2. A cell tower
    tower A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
  3. The bus stop
    jehlan_1 The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how many m2 roofing is required to cover the three walls of the sheathing, taking into account 40% of the additional coverage.
  4. Triangular prism,
    prism3s The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l).
  5. The quadrilateral pyramid
    jehlan_4b_obdelnik 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.
  6. Wall height
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
  7. Free space in the garden
    euklid The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
  8. Squares above sides
    pataVysky 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
  9. Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  10. Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  11. Rectangular base pyramid
    jehlan_4b_obdelnik Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters.
  12. What percentage
    astronaut What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
  13. Suppose
    linear_eq Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
  14. Two chords
    twochords In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.
  15. Storm and roof
    cone_church The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m2 of roof need to be repaired if 20% were damaged in a storm?
  16. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  17. Three faces of a cuboid
    cuboid The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.