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.)

Correct answer:

a =  30 cm
b =  18 cm

Step-by-step explanation:

$$\begin{gathered} S=28.26{\text{cm}}^3 \\ r=\lceil \sqrt{S\mathrm{/}\pi }\rceil =\lceil \sqrt{28.26\mathrm{/}3.1416}\rceil =3\text{ cm } \\ D=2\cdot r=2\cdot 3=6\text{ cm } \\ 15=5\cdot 3 \\ a=5\cdot D=5\cdot 6=30\text{ cm} \end{gathered}$$

$b=3\cdot D=3\cdot 6=18\text{ cm}$

Try another example

Related math problems and questions:

• Plumber
  The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
• The pool
  The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom?
• Paper squares
  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.
• Two rectangles
  I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your calc
• Rectangle diagonals
  It is given a rectangle with an area of 24 cm² a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Cuboid walls
  Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm².
• Metal washers
  Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.
• Glass panel
  A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
• Circle and rectangle
  A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
• Axial cut of a rectangle
  Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
• Rectangles
  Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
• Quadrilateral pyramid
  Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
• Aquarium
  The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edg
• Rectangular trapezium
  Calculate the perimeter of a rectangular trapezium when its content area is 576 cm² and sice a (base) is 30 cm, height 24 cm.
• Pavilion
  The rectangular pavilion with dimensions 3.5 m and 2.75 m to be paved with square tiles of side 25 cm price of CZK 22 per 1 piece or rectangular tiles with sides of 20 cm and 15 cm in the price of CZK 11 per 1 pc. Which solution is cheaper (write its pric
• Pebble
  The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
• Quadrilateral pyramid,
  A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid