Sarin’s family and Ramadan Part 11 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presenting the Math Concept, Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can learn the skills of dealing with Math Modeling, Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Perimeter, Area and Problem Solving.

You can read the posting on Sarin’s family and Ramadan and Sarin’s family celebrating Hari Raya Puasa in Welcome page about story of Sarin’s family during Ramadan and celebrating Hari Raya Puasa.

You shuold read the posting on Sarin learns Perimeter, Area and Volume in school(Math Concept) to learn the concept of Area.

Challenge yourself to solve the question before look out for the given solution‼

Upper primary school mathematics question UPQ268

Fatimah’s mother decides to change the pattern design of the carpet by including the two patterns as shown in below figure. The designs are each formed by overlapping 7 circular rings of radius 10m each. The ring in the middle in both figures passes through the centres of the 6 outer rings.

 

 

 

 

 

 

 

Use the calculator value of π to find the total area of the coloured regions in both design patterns, correct to 2 decimal places.

 

Solution:

 

 

 

 

 

 

For the design on the left,

The green eye shape portion can be shifted to as the blue shapes shown

The area of the coloured region of 1 circle is 1/3 of the area of the circle with the radius of 10m = 1/3 × π × 10 × 10 = 100/3 π

The area of the coloured region of the design on the left = 6 × 100/3 π = 200π

For the design on the right,

The size of blue regions is equal to one of the grey eye region.

The area of the coloured region of 1 circle is 2/3 of the area of the circle with the radius of 10m = 2/3 × π × 10 × 10 = 200/3 π

The area of the coloured region of the design on the right = 3 × 200/3 π = 200π

The total area of the coloured regions in both the design = 200π + 200π = 400π = 1256.64m2

 

       More Questions on Shape and Area. Click here….

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2 responses »

  1. I think that the area of the shaded part of the circles on the right should be 2/3rd of the circle x 3 and not 6. Can someone check .

    • Hi Syed,
      You are spot on! I am out of my mind when I solved the question. It should be 3 2/3rd of the circles instead of 6. The coloured area of the figure at the right is 200π and the final answer is 400π or 1256.64 cm2. I updated the solution and thanks.
      Regards,
      KCBoh

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