CBSE Class 10 Mathematics Area Related To Circle Worksheet Set 07

Short Answer Questions-: 

Question. 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 48 hours. 
Answer: \( 608\pi \) cm

Question. The side of a square is 10 cm. Find the area between inscribed and circumscribed circles of the square. 
Answer: \( 25\pi \text{ cm}^2 \)

Question. A chord of a circle of radius 14 cm subtends an angle of \( 60^\circ \) at the centre. Find the area of the corresponding minor segment of the circle. \( \left( \text{Use } \pi = \frac{22}{7} \text{ and } \sqrt{3} = 1.73 \right) \)
Answer: \( 17.90 \text{ cm}^2 \) (Approx)

Question. The area of an equilateral triangle is \( 49\sqrt{3} \text{ cm}^2 \). Taking each vertex as centre, circles are described with radius equal to half the length of the side of the triangle. Find the area of the part of the triangle not included in the circles. \( \left( \text{Take } \sqrt{3} = 1.73, \pi = \frac{22}{7} \right) \)
Answer: \( 7.77 \text{ cm}^2 \)

Question. The inner circumference of a circular track is 132 m. The track is 2.5 m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of Rs. 3.50 per metre.
Answer: Rs. 517

Question. A race track is in the form of a ring whose inner and outer circumferences are 44 cm and 66 cm respectively. Find the width of the track.
Answer: 3.5 cm

Question. A circular park is surrounded by a road 28 m wide. Find the area of the road if the circumference of the park is 880 m.
Answer: \( 27104 \text{ m}^2 \)

Long Answer Questions: 

Question. Three circles each of radius 7 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between the circles.
Answer: \( 7.86 \text{ cm}^2 \)

Question. The area of a circular playground is \( 88704 \text{ m}^2 \). Find the cost of fencing this ground at the rate of Rs. 65 per metre.
Answer: Rs. 68640

Question. The diameter of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions. 
Answer: 560

Question. Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of \( 60^\circ \). (Use \( \pi = 3.14 \))
Answer: \( 13.08 \text{ cm}^2 \)

Question. Find the difference of the area of a sector of angle \( 90^\circ \) and its corresponding major sector of a circle of radius 9.8 cm.
Answer: \( 150.92 \text{ cm}^2 \)

Question. Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of \( 90^\circ \) at the centre.
Answer: \( \left( \frac{25\pi}{4} + \frac{25}{2} \right) \text{ cm}^2 \)

Question. On a square cardboard sheet of area \( 784 \text{ cm}^2 \), four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
Answer: \( 168 \text{ cm}^2 \)

Question. All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is \( 2464 \text{ cm}^2 \). (Hint: radius of circle \( = \frac{1}{2} \) diagonal)
Answer: \( 1568 \text{ cm}^2 \)

Question. Find the number of revolutions made by a circular wheel of area \( 6.16 \text{ m}^2 \) in rolling a distance of 572 m.
Answer: 65

SECTION A

Question. Choose and write the correct option in the following questions.
(i) If the sum of the circumferences of two circles with radii \( R_1 \) and \( R_2 \) is equal to the circumference of a circle of radius \( R \), then 
(a) \( R_1 + R_2 = R \)
(b) \( R_1 + R_2 > R \)
(c) \( R_1 + R_2 < R \)
(d) None of the options
Answer: (a) \( R_1 + R_2 = R \)

Question. (ii) The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal is
(a) \( \pi : \sqrt{2} \)
(b) \( \pi : \sqrt{3} \)
(c) \( \sqrt{3} : \pi \)
(d) \( \sqrt{2} : \pi \)
Answer: (b) \( \pi : \sqrt{3} \)

Question. (iii) The area of a quadrant of a circle whose circumference is 616 cm will be
(a) \( 7546 \text{ cm}^2 \)
(b) \( 7500 \text{ cm}^2 \)
(c) \( 7456 \text{ cm}^2 \)
(d) \( 7564 \text{ cm}^2 \)
Answer: (a) \( 7546 \text{ cm}^2 \)

Question. Solve the following questions.
(i) Find the area of a square inscribed in a circle of diameter \( p \) cm.
Answer: \( \frac{p^2}{2} \text{ cm}^2 \)

Question. (ii) If the diameter of a semicircular protractor is 14 cm, then find its perimeter.
Answer: 36 cm

Question. Solve the following questions.
The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.
Answer: 3.92 cm

Question. The area of a circular playground is \( 22176 \text{ m}^2 \). Find the cost of fencing this ground at the rate of Rs. 50 per m.
Answer: Rs. 26400