Question

the radius of a Circle is double find the total increase in its area ​

Answer 1

Given,

• The radius of a Circle is double .

To Find,

• The total increase in its area .

Solution,

Area of Circle If Radius is R.

$\pi \times {R}^{2} \\ \\ \pi {R}^{2}$

Area of Circle If Radius is Double = 2R

$\pi \times {(2R)}^{2} \\ \\ \pi \times 4 {R}^{2} \\ \\ 4\pi {R}^{2}$

More Percent ;

$\frac{Difference}{Less \: \: Value} \times 100 \\ \\ \frac{4\pi {R}^{2} - \pi {R}^{2} }{\pi {R}^{2} } \times 100 \\ \\ \frac{3\pi{R}^{2}}{\pi{R}^{2}} \times 100 \\ \\ 3 \times 100 \\ 300 \:$

Required Answer,

The Total increase percent in Area is 300%

Answer 2

Given,

The radius of a Circle is double .

To Find,

The total increase in its area .

Solution,

Area of Circle If Radius is R.

\begin{gathered}\pi \times {R}^{2} \\ \\ \pi {R}^{2} \end{gathered}

π×R

2

πR

2

Area of Circle If Radius is Double = 2R

\begin{gathered}\pi \times {(2R)}^{2} \\ \\ \pi \times 4 {R}^{2} \\ \\ 4\pi {R}^{2} \end{gathered}

π×(2R)

2

π×4R

2

4πR

2

More Percent ;

\begin{gathered} \frac{Difference}{Less \: \: Value} \times 100 \\ \\ \frac{4\pi {R}^{2} - \pi {R}^{2} }{\pi {R}^{2} } \times 100 \\ \\ \frac{3\pi{R}^{2}}{\pi{R}^{2}} \times 100 \\ \\ 3 \times 100 \\ 300 \: \end{gathered}

LessValue

Difference

×100

πR

2

4πR

2

−πR

2

×100

πR

2

3πR

2

×100

3×100

300

Required Answer,

The Total increase percent in Area is 300%