Exemplar Exercise 11.3 (Areas Related to Circles) – Areas Related to Circles Practice Questions

Q1 TYPE IN THE ANSWER

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Q2 TYPE IN THE ANSWER

In Fig. 11.5, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Q3 TYPE IN THE ANSWER

Find the area of a sector of a circle of radius 28 cm and central angle 45°.

Q4 TYPE IN THE ANSWER

The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h?

Q5 TYPE IN THE ANSWER

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20m × 16m. Find the area of the field in which the cow can graze.

Q6 TYPE IN THE ANSWER

Find the area of the flower bed (with semi-circular ends) shown in Fig. 11.6.

Q7 TYPE IN THE ANSWER

In Fig. 11.7, AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use π = 3.14).

Q8 TYPE IN THE ANSWER

Find the area of the shaded field shown in Fig. 11.8.

Q9 TYPE IN THE ANSWER

Find the area of the shaded region in Fig. 11.9.

Q10 TYPE IN THE ANSWER

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

Q11 TYPE IN THE ANSWER

Find the area of the shaded region in Fig. 11.10, 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 (Use π = 3.14).

Q12 TYPE IN THE ANSWER

In Fig. 11.11, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm. to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region (Use π = 3.14).

Q13 TYPE IN THE ANSWER

In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.

Q14 TYPE IN THE ANSWER

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.

Q15 TYPE IN THE ANSWER

In Fig. 11.13, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.

Q16 TYPE IN THE ANSWER

A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle.