AREA AND PERIMETER (CDS)

Total Questions: 116

71. A circle and a square have the same perimeter. Which one of the following is correct? [2016 (II) Evening Shift]

Correct Answer: (b) The area of the circle is larger
Solution:Let r and a be the radius of a circle and side of a square respectively.

72. In an equilateral triangle another equilateral triangle is drawn inside joining the mid-points of the sides of given equilateral triangle and the process is continued up to 7 times. What is the ratio of area of fourth triangle to that of seventh triangle? [2016 (II) Evening Shift]

Correct Answer: (c) 64 : 1
Solution:Let the side of equilateral triangle be x.

73. The area of four walls of a room is 120 m² . The length of the room is twice its breadth. If the height of the room is 4 m, what is area of the floor? [2016 (II) Evening Shift]

Correct Answer: (b) 50 m²
Solution:Let l, b and hbe the length, breadth and height of the room. 

74. AD is the diameter of a circle with area 707 m² and AB = BC = CD as shown in the figure. All curves inside the circle are semi-circles with their diameters on AD. What is the cost of levelling the shaded region at the rate of ₹63 per m²? [2016 (I) Morning Shift]

Correct Answer: (c) ₹14847
Solution:Area of circle with diameter (AD)


75. A circle of 3 m radius is divided into three areas by semi-circles of radii 1 m and 2 m as shown in the figure. The ratio of the three areas A, B and C will be [2016 (I) Morning Shift]

Correct Answer: (b) 1 : 1 : 1
Solution:Given a radius of 3 m is divided in such a way that the radius of smaller semi-circle is 1 m and radius of bigger semi-circle is 2 m.


76. A truck moves along a circular path and describes 100 m when it has traced out 36° at the centre. The radius of the circle is equal to [2016 (I) Morning Shift]

Correct Answer: (c) 500/π m
Solution:Let r be the radius of the circle.

77. The number of rounds that a wheel of diameter 7/11 m will make in traversing 4 km will be [2016 (I) Morning Shift]

Correct Answer: (d) 2000
Solution:Number of rounds that a wheel of diameter D will make in traversing a distance = n D (π )

78. The base of an isosceles triangle is 300 units and each of its equal sides is 170 units. Then, the area of the triangle is [2016 (I) Morning Shift]

Correct Answer: (c) 12000 square units
Solution:Here, base = 300 units and side = 170 units

79. Four equal discs are placed such that each one touches two others. If the area of empty space enclosed by them is 150/847 sq cm, then the radius of each disc is equal to [2016 (I) Morning Shift]

Correct Answer: (d) 5/11 cm
Solution:Let the radius of the circle be r. Then, side of square ABCD = 2r

80. A circular path is made from two concentric circular rings in such a way that the smaller ring when allowed to roll over the circumference of the bigger ring, takes three full revolutions. If the area of the pathway is equal to n times the area of the smaller ring, then n is equal to [2016 (I) Morning Shift]

Correct Answer: (c) 8
Solution:Let the radius of smaller ring be r₁ and the radius of bigger ring be r.