Question

The sum of circumference and the radius of a circle is 51 cm, find the radius of the circle.​

Answer 1

Circumference + Radius = 51
2πr + r = 51
r(2π + 1) = 51
r =51/2π + 1
r=51/2(22/7) + 1
r=51/51/7
Cancel out the 51’s
r=7
Therefore, the radius of the circle is 7cm

Answer 2

$\bf \dag \frak{ \gray{Given: }}$

• Sum of radius and circumference of circle is 51 cm

$\bf \dag \frak{ \gray{To \: find: }}$

• Radius of circle

We know:-

$\bigstar \boxed{ \rm Circumference~of~circle=2\pi r}$

$\star \underline \textsf{According to question : }$

$\hookrightarrow \sf Circumference~of~circle + radius = 51$

$\hookrightarrow \sf 2\pi r + r = 51$

$\hookrightarrow \sf r( 2\pi +1) = 51$

$\hookrightarrow \sf r( 2 \times \dfrac{22}{7} +1) = 51$

$\hookrightarrow \sf r( \dfrac{44}{7} +1) = 51$

$\hookrightarrow \sf r \bigg( \frac{\frac{44 \times 7}{7} +1 \times 7}{7} \bigg) = 51$

$\hookrightarrow \sf r \bigg( \frac{\frac{44 \times \cancel7}{\cancel7} +1 \times 7}{7} \bigg) = 51$

$\hookrightarrow \sf r \bigg( \frac{\frac{44}{1} +7}{7} \bigg) = 51$

$\hookrightarrow \sf r \bigg( \dfrac{44 + 7}{7} \bigg) = 51$

$\hookrightarrow \sf r \bigg( \dfrac{51}{7} \bigg) = 51$

$\hookrightarrow \sf r = 51 \times \dfrac{7}{51}$

$\hookrightarrow \sf r = \cancel{ 51} \times \dfrac{7}{ \cancel{51}}$

$\hookrightarrow \bf r =7 \: cm$

$\therefore \underline {\textsf{\textbf{radius \: of \: circle \: is \: \red{7 \: cm}}}}$