Question

8. If the radius of the circle is increased by 20% then percentage increase in a
a) 44% b) 40% c) 144% d) 140%​

Answer 1

${\underline{\textsf{\textbf{Answer : }}}}$

The area increased is 44%

${\underline{\textsf{\textbf{ step-by-step \: explanation : }}}}$

Given :

• A radius of s circle is increased by 20%

To find :

• The increase percentage in its area.

Solution :

Let's assume the radius as x units

We know that,

➣ Area of a circle = πr²

Where,

r (radius)

So,

➠ Area of the circle = πx²

Now,

• It is told to increase in 20% of its radius

Therefore,

➣ 20% of radius

➠ (20% of x ) + x

➠ (20/100 of x) + x

➠ (x/5) + x

➠ 6x/5

➠ 6x/5 units

➣ Area after the increased radius = πr²

➠ π × (6x/5)²

➠ π × 36x²/25

➠36πx²/25

Area increased :

➠ Area of the new circle - Area of the previous circle.

➠ 36πx²/25 - πx²

➠ (36πx² - 25πx²)/25

➠ 11πx²/25

Increased percentage :

➝ Area increased/Area of previous circle × 100

➝ 11πx²/25*πx² × 100 (πx² is cancelled)

➝ 11/25 × 100 (100 is divided by 25)

➝ 11 × 4

➝ 44% increased

Hence,

The area increased is 44%

Answer 2

Given :

• If the radius of the circle is increased by 20%

To Find :

• what is the increase percentage ?

Solution :

_______________________________

Concept : -

• Area of circle = πr² where r is the radius of the circle

• To calculate the radius of a circle by using the circumference, take the circumference of the circle and divide it by 2 times π

_______________________________

Step-by-step explanation :

Let the radius of original circle is r

Then , Area of original circle = πr²

According to the Question :

the radius of the circle is increased by 20%

$: \implies \underline{ \: \mathfrak{Radius \: of \: new \: circle \: }} \sf = \: \frac{20r}{100} + r \\ \\ \\ : \implies \underline{ \: \mathfrak{Radius \: of \: new \: circle \: }} \sf = \frac{20r + 100r}{100} \\ \\ \\ : \implies \underline{ \: \mathfrak{Radius \: of \: new \: circle \: }} \sf = \cancel{\frac{120r}{100}} \\ \\ \\ : \implies \underline{ \: \mathfrak{Radius \: of \: new \: circle \: }} \sf =1.2r$

$: \implies \boxed{ \underline{ \: \mathfrak{Area \: of \: new \: circle \: = \pi R^2}}}$

Substitute all Values :

$: \implies \: \: \underline{ \: \mathfrak{Area \: of \: new \: circle \:}} \sf = \pi {(1.2r)}^{2} \\ \\ \\ : \implies \: \: \underline{ \: \mathfrak{Area \: of \: new \: circle \:}} \sf = 1.44\pi {r}^{2}$

$: \implies \: \: \underline{ \: \mathfrak{increase \: area \: \:}} \sf = \: 1.44\pi {r}^{2} - \pi {r}^{2} \\ \\ \\ \\ : \implies \: \: \underline{ \: \mathfrak{increase \: area \: \:}} \sf = \:0.44\pi {r}^{2}$

percentage increase in area :

$\sf \: : \implies \: \: \: \: \: \: \: \: \: \cancel{\frac{0.44\pi {r}^{2} }{\pi {r}^{2} }} \times 100 \\ \\ \\ \\ \\ \sf \: : \implies \: \: \: \: \: \: \: \: \:0.44 \times 100 \\ \\ \\ \\ \sf \: : \implies \: \: \: \: \: \: \: \: \:44\%$

• Hence the option a is correct