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.
Was this answer helpful?
Similar Questions
- The ratio of the length to the breath of a rectangular field is $6 : 5$. If the breath is 25 m less than the length, the perimeter of the field is:
- The ratio of the area of an equilateral triangle of side $x$ to the area of a square of side $x$ is:
- Find the perimeter of a semicircle with a radius of 7 cm. (Use $\pi = \frac{22}{7}$)
- What is the area of a rhombus, whose sides are 25 cm and one of the diagonals is 14 cm?
- A sector of a circle has a radius of $18\text{ cm}$ and a central angle of $125^\circ$. What will be its approximate perimeter?
(Use $\pi = \frac{22}{7}$) - Area of a square is equal to ten times the area of a rectangle of edge 5 cm $\times$ 8 cm. What is the perimeter of the square?
- If the length and the perimeter of a rectangle are in the ratio of 3 : 20, then its length and breadth will be in the ratio of:
- A wire in the form of a circle of radius 56 m is cut and again bent in the form of a square. What is the measure of the diagonal of the square?
- 30 ml paint is required to paint a circular plate of 20 cm radius. How much paint is required to paint a similar plate of radius 80 cm?
- The ratio of the radii of two circles is $1 : 4$. The ratio of their areas is:
Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
Need Expert Advice?
Upcoming Exams
RRB ALP
July 28, 2026
RRB Group D
August 03, 2026
Test Series
Railways
RRB NTPC Under Graduate 2026 New Mock Test Series
1459 Tests 2 Tests Free
215 Attempts
4.3(512)
English, Hindi, Telugu +7 More
More Questions from RRB NTPC
