Question

A circle of radius 1 cm, if the diameter of circle is increased by 100%, then its area is increased by
(a) 150%
(b) 200% (c) 250%
(d) 300%
​

Answer 1

The area of circle is increased by 300%

Option (d) is correct

Step-by-step explanation:

A circle of radius 1 cm.

Area $=\pi (1)^2$

$A_{old}=\pi$

Diameter of a circle is twice of radius.

Diameter = 2 cm

If the diameter of circle is increased by 100%

New Diameter = 2 + 100% of 2

New Diameter = 4

New Radius = Half of diameter

New radius = 2 cm

$A_{new}=\pi(2)^2$

$A_{new}=4\pi$

$\text{Increase percentage in area}=\dfrac{\text{difference in area}}{\text{Old area}}\times 100$

$\text{Increase percentage in area}=\dfrac{A_{new}-A_{old}}{A_{old}}\times 100$

$\text{Increase percentage in area}=\dfrac{4\pi-\pi}{\pi}\times 100$

$\text{Increase percentage in area}=300\%$

Hence, the area of circle increase by 300%

#Learn more:

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Answer 2

Answer:

(d) 300%

Step-by-step explanation:

r = 1cm

Area of circle with r 1cm = $\pi$(1)² = $\pi$

If the diameter is increased, then radius will also increase. Therefore,

r = 1 + 100/100 = 1+1 = 2cm

Area of circle with r 1cm = $\pi$(2)² = 4$\pi$

Now, to find the percentage of increase,

$\frac{4\pi - \pi }{\pi }$ x  100 = $\frac{3\pi }{\pi }$ x 100 = 3 x 100 = 300%