Math Quiz X - Of Perimeters and Areas

1. The figure shows parallelogram ABCD with BC = 4 cm, PD = 1 cm and BQ = 2 cm. If the area of ABCD is 40 sq cm, and PQ divides it into 2 parts, then the ratio of the areas of the two parts formed is :

a) 1 : 1 b) 1: 2 c) 2: 5 d) 3 : 5

2. Parallelogram ABCD has an area of 84 sq cm and DC = 12 cm. The area of the circle in sq cm is :

a) 49 b) 41.5 c) 38.5 d) 35.35

3. A wire is bent to form a perfect semicircle of radius 7 cm. It is then bent to form a square; the area of the square is :

a) 49 sq cm b) 81 sq cm c) 100 sq cm d) 121 sq cm

4. If O is the center of the semicircle, then the ratio of the areas of the shaded to the unshaded portion is :

a) 1 : 4 b) 1 : 3 c) 1 : 2 d) 1 : 1

5. A wheel of diameter 70 cm moves up a straight path inclined at 30 degs with the horizontal. The vertical height in meters attained by the wheel in 10 revolutions is :

a) 2.3 m b) 2.2 m c) 1.1 m d) 0.77 m

6. The figure shows triangle ABC, right-angled at B. If AB = 28 cm, BC = 21 cm, then the area of the circumcircle is :

a) 962.50 sq cm b) 851.49 sq cm c) 749.70 sq cm d) 700 sq cm

7. In the figure, if the circumference of each circle is 22 cm, then the area of the unshaded portion in sq cm is :

a) 63 b) 56 c) 49 d) 42

8. The ratio of the areas of the incircle to the circumcircle of a square is :

a) 1 : 4 b) 1 : 3 c) 1 : 2 d) 2 : 3

9. For the 3 circles shown, the radius of the smallest circle is half that of the medium-sized circle. The ratio of the area of the largest circle to the area of the smallest one is :

a) 14 : 1 b) 9 : 1 c) 7 : 1 d) 7 : 2

10. The figure shows a square, and its circumcircle of radius 'r'. The radius of the smaller circle, in terms of 'r' is :

a) (1 - rt2)r/8 b) (1 + rt2)r/4

c) (2 + rt2)r/8 d) (2 - rt2)r/4

---------- Answer Key ----------

1. (d) 2. (c) 3. (b) 4. (d) 5. (c)

6. (a) 7. (d) 8. (c) 9. (b) 10. (d)