Four circles are drawn side by side in a line and enclosed by a rectan

1.	Four circles are drawn side by side in a line and enclosed by a rectangle as shown below. If the radius of each of the circles is 3 cm, then calculate: (i) The area of the rectangle. (ii) The area of each circle.(iii) The shaded area inside the rectangle.
Answer» Given radius of a circle r = 3 cm Diameter of the circle = 2r = 2 x 3 = 6 cm Breadth of the rectangle = Diameter of the circle B = 6 cm Length of the rectangle L = 4 x diameter of a circle L = 4 x 6 L = 24 cm (i) Area of the rectangle = L x B sq. units = 24 x 6 cm² Area of the rectangle = 144 cm² (ii) Area of the circle = πr² sq. units = \(\frac{22}{7}\) x 3 x 3 cm² = \(\frac{198}{7}\) cm² = 28.28 cm² (iii) Area of the shaded area = Area of the rectangle – Area of the 4 circles = 144 – (4 x \(\frac{198}{7}\)) cm² = (144 – \(\frac{792}{7}\)) cm² = (144 – 113.14) cm² = 30.85 cm²

Four circles are drawn side by side in a line and enclosed by a rectangle as shown below. If the radius of each of the circles is 3 cm, then calculate: (i) The area of the rectangle. (ii) The area of each circle.(iii) The shaded area inside the rectangle.

Answer»

Given radius of a circle r = 3 cm

Diameter of the circle = 2r

= 2 x 3

= 6 cm

Breadth of the rectangle = Diameter of the circle

B = 6 cm

Length of the rectangle L = 4 x diameter of a circle

L = 4 x 6

L = 24 cm

(i) Area of the rectangle = L x B sq. units

= 24 x 6 cm²

Area of the rectangle = 144 cm²

(ii) Area of the circle = πr² sq. units

= \(\frac{22}{7}\) x 3 x 3 cm²

= \(\frac{198}{7}\) cm²

= 28.28 cm²

(iii) Area of the shaded area = Area of the rectangle – Area of the 4 circles

= 144 – (4 x \(\frac{198}{7}\)) cm²

= (144 – \(\frac{792}{7}\)) cm²

= (144 – 113.14) cm²

= 30.85 cm²