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: }}`

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• Sum of radius and circumference of circle is 51 cm

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

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• Radius of circle

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We know:-

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

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

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

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

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

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`\hookrightarrow \sf r( 2 * (22)/(7) +1) = 51 \\`

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`\hookrightarrow \sf r( (44)/(7) +1) = 51 \\`

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`\hookrightarrow \sf r \bigg( ((44 * 7)/(7) +1 * 7)/(7) \bigg) = 51 \\`

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`\hookrightarrow \sf r \bigg( ((44 * \cancel7)/(\cancel7) +1 * 7)/(7) \bigg) = 51 \\`

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`\hookrightarrow \sf r \bigg( ((44)/(1) +7)/(7) \bigg) = 51 \\`

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`\hookrightarrow \sf r \bigg( (44 + 7)/(7) \bigg) = 51 \\`

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`\hookrightarrow \sf r \bigg( (51)/(7) \bigg) = 51 \\`

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`\hookrightarrow \sf r = 51 * (7)/(51) \\`

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`\hookrightarrow \sf r = \cancel{ 51} * \frac{7}{ \cancel{51}} \\`

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

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