GCSE Edexcel Maths Area & Perimeter: The diagram shows a logo made fr

The diagram shows a logo made from three circles - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

Question 4

The diagram shows a logo made from three circles. Each circle has centre O. Daisy says that exactly $ \frac{1}{3} $ of the logo is shaded. Is Daisy correct? You... show full transcript

Worked Solution & Example Answer:The diagram shows a logo made from three circles - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

Step 1

Calculate the area of the largest circle

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Answer

The radius of the largest circle is (4 , cm). The area (A) of a circle is calculated using the formula:

$A = \pi r^2$

Thus, the area of the largest circle is:

$A = \pi (4)^2 = 16\pi \, cm^2$

Step 2

Calculate the area of the middle circle

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Answer

The radius of the middle circle is (3 , cm). Thus,

$A = \pi (3)^2 = 9\pi \, cm^2$

Step 3

Calculate the area of the smallest circle

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Answer

The radius of the smallest circle is (2 , cm). Thus,

$A = \pi (2)^2 = 4\pi \, cm^2$

Step 4

Determine the shaded area

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Answer

The shaded area is the area of the middle circle minus the area of the smallest circle:

$\text{Shaded area} = 9\pi - 4\pi = 5\pi \, cm^2$

Now, calculate the total area of all circles:

$\text{Total area} = 16\pi \, cm^2\text{ (largest)} + 9\pi \, cm^2\text{ (middle)} + 4\pi \, cm^2\text{ (smallest)} = 29\pi \, cm^2$

Finally, the fraction of the logo that is shaded is:

$\text{Fraction shaded} = \frac{5\pi}{29\pi} = \frac{5}{29}$

Since ( \frac{5}{29} ) is not equal to ( \frac{1}{3} ), Daisy is incorrect.

The diagram shows a logo made from three circles - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

Worked Solution & Example Answer:The diagram shows a logo made from three circles - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

Calculate the area of the largest circle

Calculate the area of the middle circle

Calculate the area of the smallest circle

Determine the shaded area

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