Question

The radius of a circle is increased so that circumference increases by 5%. By how much percentage will the area increase?
Explain in detail.

Answer 1

≡QUESTION≡

The radius of a circle is increased so that circumference increases by 5%. By how much percentage will the area increase?

                                                           

║⊕ANSWER⊕║

Area of circle, A = πr²

Radius of circle is increased by 5%

Increased radius = 105/100

                              = 1.05 unit

Increased area = π(105/100)² - 1π

                          = π(1.05)² - 1π

                          = 1.1025π

                            = (1.1025 - 1)π

                           = 0.1025π unit²

Percentage Increase = (0.1025/1) × 100

                                    = 10.25%