AREA AND PERIMETER (CDS)

Total Questions: 116

111. A square is inscribed in a circle of diameter 2a and another square is circumscribing circle. The difference between the areas of outer and inner squares is [2014 (I) Morning Shift]

Correct Answer: (a) a²
Solution:For inscribed circle,


112. ABC is a triangle right angled at A. AB = 6 cm and AC = 8 cm. Semi-circles drawn (outside the triangle) on AB, AC and BC as diameters which enclose areas x, y, z square units, respectively. What is x + y − z equal to? [2014 (I) Morning Shift]

Correct Answer: (c) 0
Solution:In ∆ABC, by Pythagoras theorem,


113. Consider an equilateral triangle of a side of unit length. A new equilateral triangle is formed by joining the mid-points of one, then a third equilateral triangle is formed by joining the mid-points of second. The process is continued. The perimeter of all triangles, thus formed is [2014 (I) Morning Shift]

Correct Answer: (c) 6 units
Solution:Perimeters of triangles,


114. What is the area of the major segment of a circle formed by a chord of length 5 cm subtending an angle of 90° at the centre? [2014 (I) Morning Shift]

Correct Answer: (c)
Solution:In ∆AOB, AO = OB = r [radius of circle]



115. A rectangle of maximum area is drawn inside a circle of diameter 5 cm. What is the maximum area of such a rectangle? [2014 (I) Morning Shift]

Correct Answer: (b) 12.5 cm²
Solution:Let ABCD be the rectangle inscribed in the circle of diameter DB = 5 cm


116. If AB and CD are two diameters of a circle of radius r and they are mutually perpendicular, then what is the ratio of the area of the circle to the area of the ∆ACD ? [2014 (I) Morning Shift]

Correct Answer: (b) π
Solution: