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Areas Related to Circles Worksheet for Class 10

In this page we have Class 10 Maths Worksheet for Areas Related to Circles . Hope you like them and do not forget to like , social share and comment at the end of the page.

Question 1
In a circle of radius 6cm, a chord of length 10cm makes an angle of 110^o at the centre of the circle. Find
(a)the circumference of the circle
(b)the area of the circle
(c)the length of the arc AB
(d)the area of sector OAB

Question 2
In figure, shows a sector of a circle, centre O, containing an angle θ

Prove that
Perimeter of shaded region is

Area of shaded region is

Question 3
Find the number of revolutions made by a circular wheel of area 1.54 m² in rolling a distance of 176 m.

Question 4
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions

Question 5
A chord 10cm long is drawn in a circle whose radius is 5√2 cm. Find area of both the segments. (Take π=3.14)

Question 6
A chord AB of a circle, of radius 14cm makes an angle of 60^o at the centre of the circle. Find the area of the minor segment of the circle. (Use π=22/7)

Question 7
AB is the diameter of a circle, centre O. C is a point ion the circumference such that <COB = θ. The area of the minor segment cut off by AC is equal to twice the area of the sector BOC. Prove that
alt=

Question 8
A chord of a circle subtends an angle of θ at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that

Question 9
PQRS is a diameter of a circle of radius 6cm. The lengths PQ, QR and RS are equal. Semi- circles are drawn on PQ and QS as diameters as shown in figure. Find the perimeter and area of shaded region

Question 10
In an equilateral triangle of side 24cm, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle. ( Take √3=1.732)

Question 11
A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20m × 16m. Find the area of the field in which the cow can graze.

Question 12
Four equal circles, each of radius a, touch each other. Show that the area between them is 6a²/7 (Take π=22/7)

Question 13
A rectangular park is 100m by 50m. It is surrounded by semi- circular flower beds all round. Find the cost of leveling the semi- circular flower bed at 60 paise per square metre ( Use π=3.14)

Question 14
Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh (2r + h).

Question 15
The inside perimeter of a running track is 400m. The length of each of the straight portion is 90m and the ends are semi- circles. If the track is everywhere 14m wide, find the area of the track. Also find the length of the outer running track.

Answer
(1) (i) 37.68 cm
(ii) 113.1 cm²
(iii) 11.51 cm²
(iv) 34.5 cm²
(5) 14.25 cm²
(6) 17.80cm²
(9) $12 \pi$ cm, 37.71cm²
(10) 98.55 cm²

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