The ratio of the circumferences of two circles is 2 : 3. Find the ratio of their areas. Option 1: 2 : 3 Option 2: 4 : 9 Option 3: 16 : 9 Option 4: 9 : 16

Answer: 4 : 9. Solution: Circumference = 2 r is proportional to r, so r_1 : r_2 = 2 : 3. Area = r^2 is proportional to r^2, so the area ratio is 2^2 : 3^2 = 4 : 9.

Geometry

Circles

Easy

The ratio of the circumferences of two circles is 2 : 3. Find the ratio of their areas.

2 : 3

4 : 9

16 : 9

9 : 16

✅ Correct Option: 2

Circumference $= 2\pi r$ is proportional to $r$ , so $r_1 : r_2 = 2 : 3$ . Area $= \pi r^2$ is proportional to $r^2$ , so the area ratio is $2^2 : 3^2 = 4 : 9$ .

2023: 28 May Shift 1

AB is a diameter of a circle with centre (3, 4). If coordinates of A is the point (4, 9), then find the coordinates of B.

2023: 19 June Shift 1

A, B, C, are three points on the circumference of a circle and if $AB = AC = 5\sqrt{2}$ , angle $BAC = 90$ degrees then radius of the circle is __________.

2025: 13 May Shift 1

Four circles of equal radius are drawn with centers, A, B, C and D such that ABCD is a square of side 14 cm and the circles touch externally as in the figure. The area of the shaded region bounded by the 4 circles is: (Take $\pi = \frac{22}{7}$ )

2022: 20 Aug Shift 1

Find the area of the largest circle that can be drawn inside a rectangle with sides 8 m $\times$ 9 m.

2022: 8 Aug Shift 1

The diameter of a circle whose area is numerically 110 more than its circumference is

2023: 1 June Shift 1

The circumference of a circular field is 396 m and that of the other circular field is 132 m. Find the area (in m $^2$ ) of the third circular field whose radius is the sum of the radii of the first two fields. Take $\pi = \frac{22}{7}$

The ratio of the circumferences of two circles is 2 : 3. Find the ratio of their areas.

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)