Question

Question Number: 83
Score : 1 Marko
2) If the radius of a circle is doubled, its area is
creased by
A) O 100%
B)
200%
300%​

Answer 1

Explanation:

200%

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Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a circle having a certain radius
• The Radius of Circle is doubled

To Find:

• We have to find the the percentage increase in area when radius of Circle is doubled

Solution:

Let the initial radius of Circle = R

Hence area of circle is

$\boxed{\sf{Initial \: Area = \pi \: R^2}}$

$\underline{\large\mathfrak\red{According \: to \: the \: Question:}}$

The Radius of given circle is doubled

Final Radius = 2R

$\mapsto \sf{Final \: Area = \pi \: (2R)^2}$

$\mapsto \sf{4 \: \pi \: R^2 }$

$\boxed{\sf{Final \: Area = 4 \: \pi \: R^2}}$

_________________________________

Increase in Area is given below :

$\mapsto \sf{Increase \: Area = Final - Initial</p><p>}$

$\mapsto \sf{4 \: \pi \: R^2 - \pi \: R^2</p><p>}$

$\mapsto \sf{3 \: \pi \: R^2</p><p>}$

__________________________________

Percentage increase in Area :

$\mapsto \boxed{\sf{Percentage = \dfrac{\text{Increase Area}}{\text{Initial Area}} \times 100}}$

$\mapsto \sf{ Percentage = \dfrac{3 \: \pi \: R^2}{ \pi \: R^2 } \times 100}$

$\mapsto \sf{3 \times 100}$

$\mapsto \sf{300 }$

Hence Option D is Correct

_________________________________

$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Percentage \: Increase = 300 }}$

________________________________

$\large\purple{\underline{\underline{\sf{Extra \: Information:}}}}$

• Circle is the locus of all the points moving in a plane maintaining constant distance from a fixed point known as center
• Line joining center to the a point on a circle is known as radius
• Circumference = $\sf{2 \: \pi \: R}$
• Area = $\sf{\pi \: R^2}$