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

The area of circle with radius half of original circle is 7 π cm² .

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 =
`(28* \Pi )/(\Pi )`

Or, R² = 28 cm²

∴ R =
`√(28)` cm

i.e R = 2
`√(7)` cm

So, The radius of original circle = R = 2
`√(7)` cm

Again

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

So, R' =
`(R)/(2)`

i.e R' =
`(2√(7))/(2)`

∴ R' =
`√(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 ×(
`√(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