Cutting circles

From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?

Correct answer:

n =  25
p =  21.4602 %

Step-by-step explanation:

$$\begin{gathered} r=10\text{ cm } \\ a=1\cdot 100=100\text{ cm } \\ {S}_1=a^2=100^2=10000{\text{cm}}^2 \\ D=2\cdot r=2\cdot 10=20\text{ cm } \\ {S}_2=D^2=20^2=400{\text{cm}}^2 \\ n=S_1\mathrm{/}{S}_2=10000\mathrm{/}400=25 \end{gathered}$$

$$\begin{gathered} S_3=\pi \cdot r^2=3.1416\cdot 10^2\doteq 314.1593{\text{cm}}^2 \\ p=100\cdot (S_1-n\cdot S_3)\mathrm{/}{S}_1=100\cdot (10000-25\cdot 314.1593)\mathrm{/}10000=21.4602\mathrm{\%} \end{gathered}$$

Try another example

Related math problems and questions:

• Percentage of waste
  In a square plate with side 75 cm we cut 4 same circles. Calculate the percentage of waste.
• Waste
  How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
• Cutting square
  From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?
• Lampshade
  The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when we 10% is waste?
• Tiles
  The pupils of the building school have to calculate how many roof tiles they will need to cover the roof of the house in the shape of two rectangles measuring 10 x 7.2 m. One roof tile covers a rectangular area of 22 cmx32 cm. How many tiles will they nee
• Glass mosaic
  How many dm² glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.
• 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.
• Concentric circles
  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?
• Cardboard box
  We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca
• Concentric circles and chord
  In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
• Tent
  Pyramid-shaped tent has a base square with a side length of 2 m and a height 1.7 m. How many meters of canvas is nneded to make it if for a waste should be added 10%?
• Square side
  If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?
• Tiles
  How many square tiles with an area of 121 cm² have to be ordered for the square room's paving with a side length of 2.75 meters?
• Square metal sheet
  Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
• Annulus
  Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.
• Two annuluses
  The area of the annular circle formed by two circles with a common center is 100 cm². The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.
• Square and circles
  The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.