AREA AND PERIMETER (CDS)

Total Questions: 116

11. A piece of wire of length 33 cm is bent into an arc of a circle of radius 14 cm. What is the angle subtended by the arc at the centre of the circle? [2019 (II) Evening Shift]

Correct Answer: (c) 135°
Solution:Length of arc (l) = 33 cm

12. What is the ratio of the area of a square inscribed in a semicircle of radius r to the area of square inscribed in a circle of radius r ? [2019 (II) Evening Shift]

Correct Answer: (b) 2 : 5
Solution:



13. If one side of a right-angled triangle (with all sides integers) is 15 cm, then what is the maximum perimeter of the triangle? [2019 (II) Evening Shift]

Correct Answer: (a) 240 cm
Solution:Let 2 other sides be x and y.


14. In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 10% respectively, then its perimeter increases by [2019 (I) Morning Shift]

Correct Answer: (c) 25%
Solution:Breadth of the rectangle = x

15. What is the percentage decrease in the area of a triangle if its each side is halved? [2019 (I) Morning Shift]

Correct Answer: (a) 75%
Solution:Let we have an equilateral triangle and side of triangle = x


16. Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors? [2019 (I) Morning Shift]

Correct Answer: (c)
Solution:ABCD is a square and Side of a square = a

17. Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles? [2019 (I) Morning Shift]

Correct Answer: (c) 462 cm²
Solution:Two circle are drawn with the same centre (O).

18. A rectangular red carpet of size 6 ft × 12 ft has a dark red border 6 inches wide. What is the area of the dark red border? [2019 (I) Morning Shift]

Correct Answer: (c) 17 square feet
Solution:Given,

19. The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is 4 : 5, then what is the value of k? [2019 (I) Morning Shift]

Correct Answer: (c) 4
Solution:∆ABC is right angle triangle at B

20. A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle? [2019 (I) Morning Shift]

Correct Answer: (b)
Solution:A square enclosing the circle