Let r be the original radius.
The area of the circle is equal to \pi r^{2}
When the radius is increased by 1 cm, the area becomes
\pi ( r+ 1)^{2}
Therefore,
\pi (r+1)^{2} - \pi r^{2} = 22
\pi(r^{2}+2r +1) - \pi r^{2} = 22
\pi r^{2} + 2 \pi r + \pi - \pi r^{2} = 22
2\pi r + \pi = 22
2 \frac{22}{7} r + \frac{22}{7} = 22
Dividing the equation by 22,
\frac{2}{7}r + \frac{1}{7} = 1
\frac{2r + 1}{7} = 1
2r + 1 = 7
2r = 6
r = 3
Therefore, the original radius of the circle was 3 cm
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Algebraic word problems | Lesson (article) | Khan Academy
Define a variable. · Write an equation using the variable. · Solve the equation. · If the variable is not the answer to the word problem, use the variable to calculate the ...
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