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primary 6 | Maths
| Geometry
2 Answers Below
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Date Posted: 2 years ago
Views: 563
3 small circles
= 3×42
= 126cm² (Ans)
= 3×42
= 126cm² (Ans)
See 2 Answers
Ratio of diameter is 1 : 2
So ratio of radius is also 1 : 2
Let the smaller circle's radius be u (or 1u, they are effectively the same)
Then bigger circle's radius is 2u.
Area of smaller circle
= πr²
= π × u × u
(Or πu²)
Area of bigger circle
= πr²
= π × 2u × 2u
= π × 2 × u × 2 × u
= π × 2 × 2 × u × u
= π × 4 × u × u
(Or 4πu²)
So we can see that the bigger circle's area is 4 times of the smaller circle's area.
Since the area of the smaller circle is 42cm², the bigger circle's area is 4 times of that.
This also tells you that the shaded area is 3 times of that.
So 42cm² × 3 = 126cm²
So ratio of radius is also 1 : 2
Let the smaller circle's radius be u (or 1u, they are effectively the same)
Then bigger circle's radius is 2u.
Area of smaller circle
= πr²
= π × u × u
(Or πu²)
Area of bigger circle
= πr²
= π × 2u × 2u
= π × 2 × u × 2 × u
= π × 2 × 2 × u × u
= π × 4 × u × u
(Or 4πu²)
So we can see that the bigger circle's area is 4 times of the smaller circle's area.
Since the area of the smaller circle is 42cm², the bigger circle's area is 4 times of that.
This also tells you that the shaded area is 3 times of that.
So 42cm² × 3 = 126cm²
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