Question

A circle of radius 1cm if the diameter of the circle is increased by 100% then it's area is increased by how much %

Answer 1

The area of the circle will increase by 300%.

Step-by-step explanation:

A circle has a 1 cm. of radius, i.e. 2 cm. is the diameter of the circle.

Now, the area of the circle is given by $\pi (Radius)^{2} = \pi r^{2} = \frac{22}{7} \times (1)^{2} = 3.143$ sq. cm. (Approximate.)

If the diameter of the circle is increased by 100%, then the radius will also increase by 100%.

So,  $R = r(1 + \frac{100}{100}) = 2r = 2$ cm will be the increased radius.

Hence, the area of the circle will become $\pi (Radius)^{2} = \pi R^{2} = \frac{22}{7} \times (2)^{2} = 3.143 \times 4 = 12.57$ sq. cm.

Therefore, the area of the circle will increase by percentage $\frac{12.57 - 3.143}{3.143} \times 100\% = 300\%$. (Answer)

Answer 2

Step-by-step explanation:

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