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?

Result

n =  25
p =  21.46 %

Solution:

r=10 cm a=1⋅ 100=100 cm S1=a2=1002=10000 cm2 D=2⋅ r=2⋅ 10=20 cm S2=D2=202=400 cm2 n=S1/S2=10000/400=25r=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}/S_{2}=10000/400=25
S3=π⋅ r2=3.1416⋅ 102≐314.1593 cm2 p=100⋅ (S1−n⋅ S3)/S1=100⋅ (10000−25⋅ 314.1593)/10000≐21.4602≐21.46%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})/S_{1}=100 \cdot \ (10000-25 \cdot \ 314.1593)/10000 \doteq 21.4602 \doteq 21.46 \%

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
Our percentage calculator will help you quickly calculate various typical tasks with percentages.

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

Next similar math problems:

  1. Cutting square
    circle22 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?
  2. Percentage of waste
    14 In a square plate with side 75 cm we cut 4 same circles. Calculate the percentage of waste.
  3. Circular lawn
    circular_flowerbed_1 Around a circular lawn area is 2 m wide sidewalk. The outer edge of the sidewalk is curb whose width is 2 m. Curbstone and the inner side of the sidewalk together form a concentric circles. Calculate the area of the circular lawn and the result round to 1
  4. Quatrefoil
    4listek Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
  5. Reward
    metals Janko and Peter divided the reward from the brigade so that Peter got 5/8 of the reward. What percentage of Janko's reward got?
  6. Content area and percents
    squares_8 Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%.
  7. Ace
    esicko The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
  8. The Chemistry test
    test The Chemistry test contained 8 questions, each with 3 points. Peter scored 21 points. How many percent did Peter write a test?
  9. Persons
    ball1_6 Persons surveyed:100 with result: Volleyball=15% Baseball=9% Sepak Takraw=8% Pingpong=8% Basketball=60% Find the average how many like Basketball and Volleyball. Please show your solution.
  10. Percents
    percents2_10 How many percents is 900 greater than the number 750?
  11. Art school
    skola_1 Every fifth pupil 9A goes to art school. How many percent of pupils in class 9A go to art school?
  12. The ball
    ball1_4 The ball was discounted by 10 percent and then again by 30 percent. How many percent of the original price is now?
  13. Summerjob
    tree2 The temporary workers planted new trees. Of the total number of 500 seedlings, they managed to plant 426. How many percents did they meet the daily planting limit?
  14. Frameworks is bad
    space Calculate how many percent will increase the length of an HTML document, if any ASCII character unnecessarily encoded as hexadecimal HTML entity composed of six characters (ampersand, grid #, x, two hex digits and the semicolon). Ie. space as:  
  15. Highway repair
    truck_6 The highway repair was planned for 15 days. However, it was reduced by 30%. How many days did the repair of the highway last?
  16. Percentages
    permutations_3_3 52 is what percent of 93?
  17. Profit gain
    percent_12 If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is: