Q1. The perimeter of a semicircular protractor whose radius is 'r' is:
Q2. A bicycle wheel makes 5000 revolutions in moving 11 km. The diameter of the wheel is:
Q3. The area of a circular path of uniform width $h$ surrounding a circular region of radius $r$ is:
Q4. Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference $= 2\pi \times \text{radius}$.
Q5. A pendulum swings through an angle of $30^\circ$ and describes an arc 8.8 cm in length. Find the length of the pendulum. (Use $\pi = 22/7$)
Solve on white paper.
Q6. The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days. (Take $\pi = 22/7$)
Q7. A steel wire when bent in the form of a square encloses an area of 121 cm$^2$. If the same wire is bent in the form of a circle, find the area of the circle.
Q8. An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Q9. Find the area of the shaded region in the figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. (Use $\pi = 3.14$)
Q10. A floor design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50p per cm$^2$. (Use $\sqrt{6} = 2.45$)
Q11. Case Study: Irrigation Sprinkler
In a park, a lawn sprinkler is placed in a corner of a square lawn. The sprinkler rotates and sprays water in a circular area. The radius of the spray is 14 m. The side of the square lawn is 20 m.
(i) What is the area of the lawn that is watered by the sprinkler?
(ii) What is the area of the lawn that remains dry?
(iii) If the sprinkler is moved to the center of the lawn, what area of the lawn will be watered if the spray radius is changed to 10 m? (Use $\pi = 3.14$)