Question

if radius of a circle is increased by 75% then by what percent will its circumference increase​

Answer 1

${\huge{\red{\boxed{\boxed{\boxed{\boxed{\blue{\underline{\green{\mathrm{Answer:}}}}}}}}}}}$

The circumference of the circle will increase by 75%.

Step-by-step explanation:

Given :-

• The percentage of increase in radius of the circle = 75%

To Find :-

• By what percent the circumference of the circle will increase

Solution :-

Let the initial radius of the circle be x,

New radius (after increment of 75%) = $x + (75\% \ of \ x)$

                                                              $\Longrightarrow x + (\frac{75}{100} \times x)\\\\\Longrightarrow x + \frac{75x}{100}\\\\\Longrightarrow \frac{100x}{100} + \frac{75x}{100}\\\\\Longrightarrow \frac{175x}{100} = \frac{7x}{4}$

Formula of Circumference = $2\pi r$

Initial Circumference = $2\pi x$

New Circumference (after increment in radius) = $\dfrac{2\pi \times 7x}{4} = \dfrac{14\pi x}{4} = \dfrac{7\pi x}{2}$

Increase in Circumference = New Circumference - Initial Circumference

$\Longrightarrow \dfrac{7\pi x}{2} - 2\pi x\\\\\Longrightarrow \dfrac{7\pi x}{2} - \dfrac{4\pi x}{2}\\\\\Longrightarrow \dfrac{3\pi x}{2}\\\\\\{\orange{\boxed{\mathsf{Increase \ in \ circumference = \dfrac{3\pi \it{x}}{2}}}}}$

Increase percent in circumference :-

${\huge{\mathsf{\frac{Increase \ in \ Circumference}{Actual \ Circumference}}}} \times 100\%\\\\\\\Longrightarrow \dfrac{\dfrac{3\pi x}{2}}{2\pi x} \times 100\%\\\\\\\Longrightarrow \dfrac{3\pi x}{2} \times \dfrac{1}{2\pi x} \times 100\%\\\\\\\Longrightarrow \dfrac{3\pi x}{4\pi x} \times 100\%\\\\\\\Longrightarrow 0.75 \times 100\%\\\\\\\Longrightarrow 75\%\\\\\\\\{\orange{\boxed{\boxed{\boxed{\boxed{\mathrm{\blue{Increase \ percent \ of \ circumference = 75\%}}}}}}}}$

$\leadsto {\mathfrak{\blue{Thank \ you}}}$

Answer 2

Answer:

#Hope you have satisfied with this answer.