Question

if the radius of the circle is increased by 8% then what will be the percentage increase in the area of the circle​

Answer 1

Answer:

suppose radius be r cm

area-πr^2

again radius(100+8)/100 ×r=1.08r cm

again area-(1.08r)^2π=1.1664πr^2

increase in the area of the circle--(1.1664-1)πr^2=.1664πr^2

percentage increase in area--.1664πr^2/πr^2 ×100=16.64%

Answer 2

The percentage increase in the area of the circle is 16.64 % when radius is increased by 8 %

Step-by-step explanation:

Let the radius = r cm

Therefore surface area of circle = π r²    ( ∵ area of circle is π r²  )

Now the radius is increased by = 8 %

Therefore new radius becomes

$r+ r\times 8 \% = r+\dfrac{8r}{100} = 1.08 r$

Therefore area of new circle is given by

$\pi (1.08r)^2= 1.1664 \pi r^2$

increased area = 1.1664 π r²- πr²= 0.1664 π r²

Now percentage of increased area is given by

$\text {increased area }\% =\dfrac{\text {increased area}}{\text {original area}}$

$\text {increased area } \% = \dfrac{0.1664 \pi r^2}{\pi r^2} \times 100 = 16.64 \%$

Hence the percentage increase in the area of the circle is 16.64 % when radius is increased by 8 %

#Learn more

Find the area of a circle whose diameter is 7 m

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