Quadrangular prism

Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.

Result

V =  8470 cm3
S =  2661.889 cm2

Solution:

u=22 cm a=u/2=22/2=11 2 cm≐15.5563 cm S1=a2=15.55632=242 cm2 h=35 cm V=S1⋅ h=242⋅ 35=8470=8470 cm3u = 22 \ cm \ \\ a = u / \sqrt{ 2 } = 22 / \sqrt{ 2 } = 11 \ \sqrt{ 2 } \ cm \doteq 15.5563 \ cm \ \\ S_{ 1 } = a^2 = 15.5563^2 = 242 \ cm^2 \ \\ h = 35 \ cm \ \\ V = S_{ 1 } \cdot \ h = 242 \cdot \ 35 = 8470 = 8470 \ cm^3
S2=4⋅ a⋅ h=4⋅ 15.5563⋅ 35=1540 2 cm2≐2177.8889 cm2 S=2⋅ S1+S2=2⋅ 242+2177.8889≐2661.8889=2661.889 cm2S_{ 2 } = 4 \cdot \ a \cdot \ h = 4 \cdot \ 15.5563 \cdot \ 35 = 1540 \ \sqrt{ 2 } \ cm^2 \doteq 2177.8889 \ cm^2 \ \\ S = 2 \cdot \ S_{ 1 } + S_{ 2 } = 2 \cdot \ 242 + 2177.8889 \doteq 2661.8889 = 2661.889 \ cm^2

Try another example


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.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Triangular prism
    hranol_3bokovy Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
  2. Prism 4 sides
    hranol4sreg The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
  3. Center of the cube
    center_of_cube Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
  4. Wall diagonal
    cube_6 Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
  5. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  6. Tree trunk
    tram From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
  7. Rectangular triangle PQR
    solving-right-triangles In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
  8. Diagonals in diamons/rhombus
    diamonds Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
  9. Diagonal of square
    ctverec_mo_1 Calculate the side of a square when its diagonal is 10 cm.
  10. Median in right triangle
    rt_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).
  11. Chord
    tetiva2_1 It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
  12. Two circles
    intersect_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?
  13. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  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. Tv screen
    tv2 The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
  16. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  17. Windbreak
    vichrica A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?