Class 10 - Chapter 11: Areas Related to Circles

Section A (1 Mark each)

Q1. The area of the circle that can be inscribed in a square of side 6 cm is:

(a) $36\pi$ cm$^2$ (b) $18\pi$ cm$^2$ (c) $12\pi$ cm$^2$ (d) $9\pi$ cm$^2$

Q2. The area of the square that can be inscribed in a circle of radius 8 cm is:

(a) 256 cm$^2$ (b) 128 cm$^2$ (c) $64\sqrt{2}$ cm$^2$ (d) 64 cm$^2$

Q3. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is:

(a) 31 cm (b) 25 cm (c) 62 cm (d) 50 cm

Q4. Assertion (A): The area of the largest triangle that can be inscribed in a semicircle of radius $r$ is $r^2$.
Reason (R): The height of the largest triangle inscribed in a semicircle is the radius $r$ and the base is the diameter $2r$.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Solve on white paper.

Q6. Find the area of the shaded region in the figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Solve on white paper.

Q7. A square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use $\pi = 3.14$)

Solve on white paper.

Section C (3 Marks each)

Q8. AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O. If $\angle AOB = 30^\circ$, find the area of the shaded region.

Solve on white paper.

Q9. On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of the remaining portion of the handkerchief.

Solve on white paper.

Section D (5 Marks)

Q10. A racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:
(i) The distance around the track along its inner edge.
(ii) The area of the track.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study:

A rectangular park is 100 m by 50 m. It has semi-circular flower beds on the two smaller sides.

(i) Find the perimeter of the park.

(ii) Find the area of the park.

(iii) Find the cost of turfing the park at the rate of Rs 10 per m$^2$.

Solve on white paper.