Question
The circumference of a circle is $30 \pi$ cm. What is its area (in $\text{cm}^2$)?
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper (8-Mar-2021) (Shift 2)
The correct answer is
$225 \pi$
Finding Circle Area from Circumference
We are given the circumference of a circle and need to find its area.
Calculate Circle Radius from Circumference
The formula for the circumference ($C$) of a circle is $C = 2 \pi r$, where $r$ is the radius.
- Given: Circumference $C = 30 \pi$ cm.
- Set up the equation: $2 \pi r = 30 \pi$.
- Solve for the radius ($r$): Divide both sides by $2 \pi$. $ r = \frac{30 \pi}{2 \pi} $ $ r = 15 \text{ cm} $
Calculate Circle Area from Radius
The formula for the area ($A$) of a circle is $A = \pi r^2$. Now that we have the radius, we can calculate the area.
- Radius $r = 15$ cm.
- Substitute the radius into the area formula: $ A = \pi (15)^2 $ $ A = \pi (225) $ $ A = 225 \pi \text{ cm}^2 $
The area of the circle is $225 \pi$ cm$^2$. This matches Option B.
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