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RD Chapter 15- Areas Related to Circles Ex-15.4 Interview Questions Answers

Question 1 : A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in the figure. If AB = 60 m and BC = 28 m, find the area of the plot.

Answer 1 :

Plot is formed of a rectangle ABCD and one semicircle on BC as diameter
∴  AB (l) = 60 m,
BC (b) = 28 m
∴ Radius of semicircle (r) = (1/2) BC
= 1/2 x 28 = 14m
Area of plot = area of rectangle ABCD + area of semicircle

Question 2 : A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take π = 22/7).

Answer 2 :

Length of rectangle (l) = 36 m 49
and width (b) = 24.5 =  49/2 m

Question 3 : Find the area of the circle in which a square of area 64 cm2 is inscribed. (Use π = 3.14)

Answer 3 :


Question 4 : A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m have been cut. Find the area of the remaining part.

Answer 4 :

Length of rectangular piece (l) = 20 m
and width (b) = 15m
Radius of each quadrant (r) = 3.5 m = 7/2 m
Now area of the rectangle = l x b = 20 x 15 = 300 m²
and area of 4 quadrants = 4 x (1/4) πr²

Question 5 : In the figure, PQRS is a square of side 4 cm. Find the area of the shaded square.

Answer 5 :

Side of the square PQRS (a) = 4 cm
∴ Area of total square = a² = 4×4=16 cm²
Radius of each of the four quadrants at the corners = 1 cm

Question 6 : Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed ? (See figure)

Answer 6 :

side of square (a) = 50 m
∴ Area of the square field = a² = (50)² m² = 2500 m²
Radius of each quadrant (r) = 50/2 = 25 m

Question 7 : A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m x 16 m, find the area of the field in which the cow can graze. [NCERT Exemplar]

Answer 7 :

Let ABCD be a rectangular field of dimensions 20 m x 16 m.
Suppose, a cow is tied at a point A.  Let length of rope AE = 14m =r (say).