Sarin learns Perimeter, Area and Volume in school part 112 (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 presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can acquire the skill of dealing with the Math Modeling, the Math Problem Solving and the 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 Shapes and Area

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

Read also the posting on Sarin learns Shapes and Solids in school (Math Concept) to know about shapes.

Challenge yourself with the question before look out for the given solution‼!

Upper primary school mathematics question UPQ525

The figure below is made up of four identical small circles enclosed in a large circle. The diameter of the large circle is 84 cm. What is the total area of the orange regions?

(Take π = 22/7)

UPQ525-1

Solution:

UPQ525-2

The diameter of the small circle = 84 ÷ 2 = 42 or 21cm for radius

The area of a small eye = ½ of the area of a small circle – the area of the green triangle

The area of a small eye = ½ × π × 21 × 21 – ½ × 42 × 21 = 252 cm2

The area of the orange regions = The area of the big circle – the area of the four small circle + the area of the four eyes

The area of the orange regions = π × 42 × 42 – 4 × π × 21 × 21 + 4 × 252 = 1008 cm2

Alternative solution(1):

UPQ525-3

 

The area of the orange region = the area of the big circle – the area of 4 small semicircle – the area of blue square

The diameter of the small circle = 84 ÷ 2 = 42 cm

The area of the blue square = 42 × 42 = 1764 cm2

The area of a small semicircle = ½ × π × 21 × 21 = 693 cm2

The area of the orange region = π × 42 × 42 – 4 × 693 – 1764 = 1008 cm2

Alternative solution(2):

UPQ525-4

Consider a quarter of the big circle

The area of a quarter of orange region = The area of a quadrant of big circle – the area of a small semicircle – the area of the yellow square

The area of the yellow square = 21 × 21 = 441 cm2

The area of a small semicircle = ½ × π × 21 × 21 = 693 cm3

The area of a quadrant of the orange region = ¼ × π × 42 × 42 – 441 – 693 = 252 cm2

The area of the orange region = 4 × 252 = 1008 cm2

   More Questions on Area. Click here….

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4 responses »

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  3. Pingback: Can You Solve This Problem For 12 Year Olds In Singapore? 4 Overlapping Circles Puzzle | TOP TEN SG : Sibei Good . Must Share

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