Answer :
Answer:
The area of circle with radius half of original circle is 7 π cm² .
Step-by-step explanation:
Given as :
The Area of original circle = 28 π square centimeter
Let The radius of original circle = R
Let The area of circle with radius half of original circle = A square centimeters
Let The radius of circle with radius half of original circle = R'
Now, According to question
∵ Area of original circle = π × radius²
So, 28 π cm² = π × R²
Or, R² = [tex]\frac{28\times \Pi }{\Pi }[/tex]
Or, R² = 28 cm²
∴ R = [tex]\sqrt{28}[/tex] cm
i.e R = 2 [tex]\sqrt{7}[/tex] cm
So, The radius of original circle = R = 2 [tex]\sqrt{7}[/tex] cm
Again
∵ The radius of circle with radius half of original circle = R'
So, R' = [tex]\dfrac{R}{2}[/tex]
i.e R' = [tex]\frac{2\sqrt{7}}{2}[/tex]
∴ R' = [tex]\sqrt{7}[/tex] cm
So, The area of circle with radius half of original circle = π × R'²
i.e A = π × R'²
Or, A = π ×([tex]\sqrt{7}[/tex]) ²
or, A = π × 7
So, The area of circle with radius half of original circle = 7 π cm²
Hence The area of circle with radius half of original circle is 7 π cm² . Answer