Gujarat Board Solutions Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.3

Gujarat Board Solutions Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.3

Gujarat Board Textbook Solutions Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.3

Question 1.
Find the area of shaded region in the given figure. If PQ = 24 cm, PR = 7 cm, and O is the centre of the circle. (CBSE 2012)

Question 4.
Find the area of the shaded region in the given 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. (CBSE 2016)

Question 5.
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in figure. Find the area of the remaining portion of the square.

Question 6.
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design (Shaded region).

Question 7.
In figure, ABCD is a square of side 14 cm with centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of shaded region.

Question 8.
Figure depicts 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.

Question 9.
In figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. (CBSE 2000, 2010, 2013)

Question 10.
The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is dräwn with radius equal to half the length of side of the triangle (see figure). Find the area of shaded region. (Use π = 3.14 and √3 = 1.73205)

Question 11.
On a square handkerchief, nine circular designs each of radius 7 cm are made (see figure). Find the area of the remaining portion of the handkerchief.

Question 12.
In figure OACB is a quadrants of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) quadrant OACB
(ii) shaded region.

Question 13.
In figure, a square OABC is inscribed in a quadrant OPBQ If OA = 20 cm, find the area of the shaded region.

Question 14.
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see figure). If ∠AOB = 30°, find the area of shaded region.

Question 15.
In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of shaded region.

Question 16.
Calculate the area of the diagonal region in figure common between the two quadrants of circles of radius 8 cm each.

Solution:

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