Question

The area of a circle is increased by 22 cm” when its radius is increased by 1 cm. The original radius of the circle is
(a) 6 cm
(b) 3.2 cm
(c) 3 cm
(d) 3.5 cm


Please make me explain Step-by-step..The first correct answer will be marked as the brainleast ​

Answer 1

Answer:

Option C is the correct answer.

Step-by-step explanation:

According to the question,

π* (r + 1) ^ 2 - π* r ^ 2 = 22

⇒ π(²+2r+1-²) = 22

2π* r + π = 22

22/7 * (2r + 1) = 22

2r + 1 = 7

2r= 6⇒ r = 3 cm.

Answer 2

Given: The area of a circle is increased by $22$cm when its radius is increased by $1$cm.

We have to find the original radius of the circle.

As we know that the formula to calculate the area of the circle is$A=\pi r^{2}$.

We are solving in the following way:

According to the given statement, we can write:

$\begin{array}{l}=>\pi(r+1)^{2}-\pi r^{2}=22 \\\Rightarrow \pi\left(r^{2}+2 r+1-r^{2}\right)=22 \\\Rightarrow 2 \pi r+\pi=22\end{array}$

$\begin{array}{l}\Rightarrow \quad \frac{22}{7}(2 \mathrm{r}+1)=22 \\\Rightarrow 2 \mathrm{r}+1=7\end{array}$

Solving the above equation further we get,

$\begin{array}{l}\Rightarrow 2 r+1=7 \\\Rightarrow 2 r=6 \ \\\Rightarrow r=3 \mathrm{~cm}\end{array}$

Hence, the original radius of the circle will be $3$cm.