Answer: r = 7
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
π is a constant whose value is 3.14
r represents the radius of the circle.
From the information given
Diameter of the big circle = 20 cm
Radius = diameter/2
Radius = 20/2 = 10
Area of big circle = π × 10² = 100π
Radius of small circle = r
Area of small circle = πr²
Area of big circle - area of small circle = shaded area
Therefore
100π - πr² = 51π
π(100 - r²)/= 51π
Dividing through by π, it becomes
100 - r² = 51
r² = 100 - 51 = 49
r = √49 = 7
