Circles – Area & Circumference Quiz - ICSE Class 9 Mathematics

Free practice quiz: Circles – Area & Circumference (ICSE Class 9 Mathematics). 41 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 9 Mathematics practice quiz has 41 multiple-choice questions on Circles – Area & Circumference, and 41 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. A circular park has a radius of 21 meters. What is its circumference?

   1. 132 meters
   2. 66 meters
   3. 264 meters
   4. 42 meters
   Show answer

   Answer: A. 132 meters

   The circumference of a circle is given by the formula $C = 2 \pi r$. Given $r = 21$ meters and $\pi \approx \frac{22}{7}$, the circumference is $C = 2 \times \frac{22}{7} \times 21 = 2 \times 22 imes 3 = 132$ meters.

2. The ratio of the radii of two circles is 2:3. What is the ratio of their areas?

   1. 2:3
   2. 4:9
   3. 8:27
   4. 2:5
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   Answer: B. 4:9

   Let the radii of the two circles be $r_1$ and $r_2$. We are given $\frac{r_1}{r_2} = \frac{2}{3}$. The area of the first circle is $A_1 = \pi r_1^2$ and the second is $A_2 = \pi r_2^2$. The ratio of their areas is $\frac{A_1}{A_2} = \frac{\pi r_1^2}{\pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2 = \left(\frac{2}{3}\right)^2 = \frac{4}{9}$.

3. If the circumference of a circle is doubled, by what factor does its area increase?

   1. 2
   2. 4
   3. 8
   4. 16
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   Answer: B. 4

   Let the initial circumference be $C_1 = 2 \pi r_1$ and the initial area be $A_1 = \pi r_1^2$. If the circumference is doubled, the new circumference $C_2 = 2 C_1 = 4 \pi r_1$. Let the new radius be $r_2$. Then $C_2 = 2 \pi r_2$. So, $4 \pi r_1 = 2 \pi r_2 \implies r_2 = 2 r_1$. The new area is $A_2 = \pi r_2^2 = \pi (2 r_1)^2 = \pi (4 r_1^2) = 4 (\pi r_1^2) = 4 A_1$. Therefore, the area increases by a factor of 4.

4. A goat is tied to a stake at the center of a circular field of radius 14 meters. If the goat can graze an area of 616 sq meters, what is the radius of the area it can graze?

   1. 7 meters
   2. 14 meters
   3. 21 meters
   4. 28 meters
   Show answer

   Answer: B. 14 meters

   The area the goat can graze is a circle. We are given the area grazed $A = 616$ sq meters. The formula for the area of a circle is $A = \pi r^2$. Using $\pi = \frac{22}{7}$, we have $616 = \frac{22}{7} r^2$. Solving for $r^2$: $r^2 = 616 imes \frac{7}{22} = 28 imes 7 = 196$. So, $r = \sqrt{196} = 14$ meters. The radius of the field (14 meters) matches the radius of the area the goat can graze, meaning the goat can graze the entire field if its rope is long enough. The question asks for the radius of the area it can graze, which is calculated to be 14 meters. The radius of the field being 14 meters is a condition, not necessarily the limit of grazing. The rope length determines the grazing area. If the rope is shorter than 14m, it can't graze the entire field. The question implies the rope length is such that it can graze 616 sq m. So we calculate the radius from the area. The radius of the field is given as 14 meters. This means the goat's rope length is at least 14 meters. If the rope length were shorter than 14m, then the grazing area radius would be the rope length. However, the calculation shows the radius of the grazing area is exactly 14 meters. So the rope length is exactly 14 meters.

5. The diameter of a circle is 7 cm. What is its circumference?

   1. 7 cm
   2. 11 cm
   3. 22 cm
   4. 154 cm
   Show answer

   Answer: C. 22 cm

   The diameter of the circle is $d = 7$ cm. The circumference of a circle is given by the formula $C = \pi d$. Using $\pi \approx \frac{22}{7}$, the circumference is $C = \frac{22}{7} imes 7 = 22$ cm.

More questions in this quiz

Answers and explanations are in the full quiz.

1. The area of a circle is $154$ square centimeters. What is its radius?
2. If the diameter of a circle is 28 cm, what is its area?
3. The circumference of a circle is 88 cm. What is its diameter?
4. What is the ratio of the circumference of a circle to its diameter?
5. The area of a circle is 616 sq cm. What is its circumference?
6. A circular disc has a radius of 10 cm. If the radius is increased by 10%, what is the percentage increase in its area?
7. The ratio of the radii of two circles is 2:3. What is the ratio of their circumferences?
8. A wheel of radius 0.5 meters rolls without slipping along a straight line. How much distance does it cover in one complete revolution?
9. The area of a semicircle is 77 sq cm. What is its radius?
10. A square is inscribed in a circle of radius 7 cm. What is the area of the square?
11. A circle is inscribed in a square of side 10 cm. What is the area of the circle?
12. Two concentric circles have radii 5 cm and 12 cm. What is the area of the ring between them (annulus)?
13. The area of a circle is increased by 44%. By what percentage is its radius increased?
14. A circular ring has an outer radius of 15 cm and an inner radius of 10 cm. What is the area of the ring?
15. The difference between the circumference and diameter of a circle is 30 cm. Find the radius of the circle.
16. A circular garden has a perimeter of 132 meters. What is its area?
17. The area of a circle is 154 sq cm. What is the circumference of the circle?
18. The area of a circle is numerically equal to its circumference. What is the radius of the circle?
19. A circular wire of radius 28 cm is bent to form a square. What is the side length of the square?
20. The area of a circular sector with radius 10 cm and angle $60^\circ$ is:
21. The circumference of a circle is 22 cm. What is its area?
22. The circumference of a circle is increased by 50%. By what factor does its area increase?
23. A square of side 10 cm is circumscribed about a circle. What is the area of the circle?
24. The area of a circle is 1386 sq cm. What is its circumference?
25. The ratio of the circumference of a circle to its perimeter is 1:1. What is the perimeter of the circle if its area is 154 sq cm?
26. A circular path of width 3.5 meters runs around a circular field whose circumference is 176 meters. What is the area of the path?
27. The area of a circle is increased by 69%. By what percentage is its circumference increased?
28. The circumference of a circle is 11 cm. What is its area?
29. If the circumference of a circle is 44 cm, what is its diameter?
30. A square is circumscribed by a circle of radius 10 cm. What is the area of the square?
31. The area of a circle is $25\pi$ sq cm. What is its circumference?
32. A circle is inscribed in an equilateral triangle of side 12 cm. What is the radius of the circle?
33. The circumference of a circle is 132 cm. What is its radius?
34. The radius of a circle is increased by 20%. What is the percentage increase in its circumference?
35. The area of a circle is 616 sq cm. What is its radius?
36. The circumference of a circle is 44 cm. What is its radius?

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