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64/140 Marks
The diagram shows a circle inside a square.
a
Work out the area of the circle.
16 cm
B
Optional working
Ansi
cm²
+

Answer 1

The area of the circle is 201.06 square centimeters.

To find the area of the circle inscribed within the square, we need to know the relationship between the circle and the square.

Typically, when a circle is inscribed within a square, the diameter of the circle is equal to the side length of the square.

This means that the radius of the circle is half the side length of the square.

If the side length of the square is 16 cm, then the diameter of the circle (which is also the diagonal of the square) is also 16 cm.

Therefore, the radius of the circle is half of the diameter, which is

`(16)/(8) = 8cm`

The formula to find the area of a circle is

π×radius^2

Substituting the radius (8 cm) into the formula:

Area of the circle = π×
`8^2`

Area of the circle= π × 64

Area of the circle= 3.14 × 64

Area of the circle ≈ 201.06 square centimeters

The area of the circle is 201.06 square centimeters.

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