Pagans

Elena cut out same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagans occupied 28.26 cm2 of the bottom of the sheet. What dimensions does the bottom of the sheet have? (Calculate with π = 3,14.)

Result

a =  30 cm
b =  18 cm

Solution:

S=28.26 cm3 r=⌈S/π⌉=⌈28.26/3.1416⌉=3 cm D=2⋅ r=2⋅ 3=6 cm 15=5⋅ 3 a=5⋅ D=5⋅ 6=30=30  cm S = 28.26 \ cm^3 \ \\ r = \lceil \sqrt{ S/\pi } \rceil = \lceil \sqrt{ 28.26/3.1416 } \rceil = 3 \ cm \ \\ D = 2 \cdot \ r = 2 \cdot \ 3 = 6 \ cm \ \\ 15 = 5 \cdot \ 3 \ \\ a = 5 \cdot \ D = 5 \cdot \ 6 = 30 = 30 \ \text{ cm }
b=3⋅ D=3⋅ 6=18=18  cm b = 3 \cdot \ D = 3 \cdot \ 6 = 18 = 18 \ \text{ cm }

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




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

Next similar math problems:

  1. Children's home
    jablka The children's home received a gift to Nicholas of 54 oranges, 81 chocolate figurines, and 135 apples. Every child received the same gift and nothing was left. a) How many packages could be prepared? b) what did the children find in the package?
  2. Lawns
    grass Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?.
  3. Cable
    wire Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.
  4. Inscribed circle
    vpisana The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
  5. Diameter
    circles2_1 What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
  6. Circle area
    circle3 Calculate the circle area with a radius of 1.2 m.
  7. Inscribed rectangle
    rectangle_inside_circle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
  8. Tiles
    kachlicky Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
  9. A rectangle
    rectangle_12 A rectangle has an area of 36 cm2. What could the length and width of rectangle be?
  10. Rectangle
    squares2_3 Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.
  11. Paper squares
    stv The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
  12. Rectangle 45
    rectangles2_4 The perimeter of a rectangle is 60cm. If the length of the rectangle is 20cm. a)find the width b)find the area.
  13. Troops
    army If the general sorts troops into the crowd by nine left 6. How many soldiers has regiment if we know that they are less than 300?
  14. Tiles
    dlazba2 It is given an area of 5m x 4m One tile is 40 x 40 cm How many tiles are needed in an area of 5 m x 4 m? And how many tiles need to be cut (if it not possible for the tiles to fall exactly)?
  15. Expression
    expr_2 Solve for a specified variable: P=a+4b+3c, for a
  16. Salary
    czk_koruna Mr. Vesely got for work 874 CZK (Czech Republic Koruna). Mr. Jaros got twice less than Mr. Vesely. How much CZK got Mr. Jaros?
  17. Chebyshev formula
    ChebyshevSpiral To estimate the number of primes less than x is used Chebyshev formula: ? Estimate the number of primes less than 30300537.