Mathematics
Class-X
2015-2016
ASSESSMENT SHEET
Q. 1. The circumference of a circle is 123.2cm. Calculate : i.
The radius of the circle. ii.
The area of the circle, correct to nearest cm
2
, iii.
the effect on the area of the circle, if the radius is doubled
Q. 2. The sum of diameters of two circles is 1.96m and the difference of their circumferences is
0.88m. Find the radii of two circles.
Q. 3. Two circles touch externally. The sum of their areas is their centers is 10cm. Find the radii of two circles. and the distance between
Q. 4. The length of a wire which is tied as a boundary of a semi-circular park is 108m. Find the radius of the semi-circular park and area of the park.
Q. 5. The wheel of a cart is making 5 revolution per second. If the diameter of the wheel is
84cm, find its speed in Km/hr. Give your answer, correct to nearest km.
Q. 6. A bucket is raised from a well by means of a rope which is bound round a wheel of diameter 77cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of
1.1m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket
Q. 7. In the given figure, the area enclosed between the concentric circles is 770cm
2
. If the radius of the outer circle is 21cm, calculate the radius of the inner circle
Q. 8. The shaded area in the given figure, between the circumferences of two concentric circles is 346.5cm
2
. The circumference of the inner circle is 88cm. Calculate the radius of the outer circle.
Sudheer Gupta .
Be positive and constructive. 
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Mathematics
Class-X
2015-2016
Q. 9. In the given figure, the shape of the top of a table in a restaurant is that of a segment of a circle with centre O and , BO = OD = 60cm. Find i.
The area of the top of the table ii.
The perimeter of the table.
Q. 10. A sheet is 11cm long and 2cm wide. Circular pieces 0.5cm in diameter are cut from it to prepare discs. Calculate the number of discs that can be prepared.
Q. 11. AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of the shaded portion is 308cm 2 , calculate i.
The length of AC and ii.
The circumference of the circle. (
Sudheer Gupta .
)
Be positive and constructive. 
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Mathematics
Class-X
2015-2016
Q. 12. PQRS is a diameter of a circle of radius 6cm. The length PQ, QR and RS are equal.
Semicircles are drawn on PQ and QS as diameters as shown in the figure. Find the area of the shaded region.
Q. 13. In the figure, O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54cm and BC = 10cm, find the area of the shaded region.
Q. 14. In the figure, AB is the diameter of the circle with centre O and OA = 7cm. Find the area of the shaded region.
Q. 15. A horse is tethered to one corner of a field which is the shape of an equlateral triangle of side 12m. If the length of the rope is 7m, find the area of the field which the horse cannot graze
Sudheer Gupta .
Be positive and constructive. 
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Mathematics
Class-X
2015-2016
Q. 16. Calculate the area of the shaded portion. The quadrant shown in the figure are each of radius 7cm
Q. 17. In the figure, AOB is a quadrant of a circle of radius 14cm. A semi-circle with AB as diameter is drawn. Find the area of the shaded region.
Q. 18. The figure, shows a running track surrounding a grassed encloser PQRSTU. The enclosure consists of a rectangle PQST with a semi-circular region at each end. PQ = 200m, PT
= 70m. i.
Calculate the area of the grassed enclosure in m
2
. ii.
given that the track is of constant width 7m. Calculate the outer perimeter ABCDEF of the track.
Q. 19. From a trapezium ABCD, in which AB || DC and removed.
Given AB = BC = 3.5, DE = 2cm. Calculate the remaining area.
, quarter circle BFEC is
Answers
Sudheer Gupta .
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Page 4

1. (i) 19.6cm
(ii) 1207cm 2
(iii) 4 times
3. 3cm, 7cm
5. 48km
7. 14cm
9. (i) 8478cm
2
(ii) 261.3cm
11. (i) 28 cm
(ii) 88 cm
13. . 770cm
2
15. 36.702m
2
17. 98cm
2
19. 6.125cm
2
Mathematics
Class-X
2. 56cm,42cm
4. 21m, 693m
6. 40
8. 17.5cm
10. 112
12. 37.71cm
2
14. 66.5cm
2
16. 42cm
2
18. (i) 17850m
2
(ii) 664m
2015-2016
Sudheer Gupta .
Be positive and constructive. 
Page 5