Question

the area of a circle is 28pi cm^2. find the area of a circle with a radius half the length of the original circle.

Answer 1

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 = $\frac{28\times \Pi }{\Pi }$

Or, R² = 28 cm²

∴  R = $\sqrt{28}$ cm

i.e R = 2 $\sqrt{7}$ cm

So, The radius of original circle = R =  2 $\sqrt{7}$ cm

Again

∵ The radius of circle with radius half of original circle = R'

So, R' = $\dfrac{R}{2}$

i.e  R' = $\frac{2\sqrt{7}}{2}$

∴  R' =  $\sqrt{7}$ cm

So, The area of circle with radius half of original circle =  π × R'²

i.e A = π × R'²

Or, A = π ×($\sqrt{7}$) 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