A circle of radius 2 cm, if the diameter of circle is increased by 100%, then its area is increased by
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Step-by-step explanation:
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Secondary School Math 50 points
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%
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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%