Area Related To
Circles (for average and gifted
students )
Class: - 10th
1. A
copper wire, when bent in the form of square, encloses an area of 484 cm2.
If the
Same
wire is bent in the form of a circle ,
Find the area encloses by it . (616 cm2
)
2. Two circles touch externally. The sum of their
areas is 130p
cm2 and the distance
Between
their centers is 14cm. Find the radii of the circles. (11cm, 3cm)
3. Two
circles touch internally. The sum of their areas is 116p cm2 and the
distance
Between their centers is 6cm. Find the radii
of the circles. (10cm, 4 cm)
4. A
bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the
Wheel.
(70 cm)
5.
In figure, ABCD is a square inscribed in a
circle of radius 7cm. Calculate: 
( a) the area of the square ( b) area of the shaded
portion
6. The inside perimeter of practice running track
with semi circular ends and
Straight parallel sides are 312 m. The length
of the straight portion of the
track
is 90m. If the track has uniform width of 2m throughout. Find its area
.7. Find the radius
of the circle if an arc of angle 40° has length 4p m.
Hence find the
Area of the sector formed by this
arc.
8. Four cows are tethered at four corners of a
square field of side 70m so that they can
Reach each other. What area of the field will
remain ungrazed?
9. A chord 10cm long is drawn in a circle whose
radius is Ö50
cm. Find the area of
Segments.
10. The short and long hand of a clock
are 4cm and 6cm long respectively. Find the sum 
Distance travelled by their tips
in two days.
11. A crescent is formed by two circles which touch at A. C
is the center of the large
Circle. The width of crescent at BD is 9cm and at EF it is 5cm. Find the
area of the 
Shaded region.
12. The radius of a
circle is 2m. What is the radius of another circle whose area is 9
Times that of the first ?
13. A bucket is raised from a well by means of a rope which
is wound round a wheel of
Diameter 77cm.
Given that the bucket ascends in 1 min. 28 seconds with a uniform
Speed of 1.1 m/s
. Calculate the number of complete revolutions the wheel makes in
Raising the
bucket.
( 40 revo. )
14. There are two concentric circular tracks of radii 100m
and 102 m respectively. A runs
On
the inner track and goes once round the track in 1min. 30 sec; while B runs on
the
Outer track in 1min. 32 sec. Who runs
faster? ( A runs
faster )
15. In given figure, find the area of
shaded portion. (85.56cm2)
16. 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 Ö3 = 1.73 and p =
3.14 )
( 98.4 cm2) A B
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 |
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17. Find the shaded portion in given
figure.
D
18. A pendulum swings through an angle of 30’ and describes
an arc 8.8cm in length. Find the length of the pendulum?
19. The minute hand of the clock is 10cm long. Find the area
of the face of the clock described by the minute hand between 9am 9:35am?
20. An arc of circle is of length 5
cm and the sector it bounds has an area of 20
cm sq.. Find the radius of the circle?
cm and the sector it bounds has an area of 20 cm sq.. Find the radius of the circle?
21. An elastic belt is placed round the rim of a pulley of
radius 5cm. one point on the belt is pulled directly away from the centre O of
the pulley until it is at P, 10cm from O. Find the length of belt that is in
contact with the rim of the pulley, also find the shaded area?
22. In a circle with centre O and radius 5cm, AB is the
chord of length 5
cm. Find the area of sector AOB ?
cm. Find the area of sector AOB ?
23. The perimeter of a sector of circle of radius 5.2cm is
16.4cm. Find the area of sector?
24. Find the area of sector of a circle whose radius is 14cm
and angle of sector 45’?
25. A sector is cut from a circle of radius 21cm an angle of
sector 150’. Find the length of its arc and area?
26. The minute hand of the clock is 
cm. Find the area described by
the minute hand on the face of clock between 7am to 7:05am?
cm. Find the area described by
the minute hand on the face of clock between 7am to 7:05am?
27. The area of a sector of a circle of radius 5cm is 5cm sq. Find the angle contained
by the sector?
cm sq. Find the angle contained
by the sector?
Surface
Area And Volume
1. A
semi circular sheet of metal of diameter 28cm is bent into an open conical cup.
Find the depth and capacity of
The cup. (12.12cm, 622.16cm3
)
2.
How many spherical lead shots each 4.21cm in diameter can be obtained
from a rectangular solid lead with
Dimension 66cm, 42cm and 21cm? ( 1500)
3. A toy is in the form of a cone mounted on a
hemi-sphere. The diameter of the base of the cone is 18cm and its
Height is 20cm. Calculate the surface area
of the toy. (Take p = 3.14) (932.58 cm2)
4 A rectangular
sheet of paper 44cm x 18cm is rolled along its length and a cylinder is formed.
Find the volume of
The cylinder. (Take p = 22/7 ) ( 2772 cm3)
5.
A circus tent is in the form of a right circular cylinder and a right
circular cone above it. The diameter and the
Heights of the cylindrical part
of the tent are 126m and 5m respectively. The total height of the tent is 21m.
Find
The total surface area of the
tent.(Take p = 22/7)
( 14850 m2)
6. A building is in the form of a cylinder
surmounted by a hemi spherical vault dome which contains 17.7m3 of
air
And its internal diameter is equal to the height
of the crown of the vault above the floor. Find the height of the
Building. (Take p = 22/7)
(3m)
7. In the given figure, a cone of radius 10cm is
divided into two parts by drawing a plane through the mid-point of
Its axis parallel
to its base. Compare the volumes of the two parts. ( 1: 7)
8. The diameter of a
sphere is 42 cm. It is melted and drawn into a cylindrical wire of 28cm in
diameter. Find the length of the wire. (63cm)
9. If h, c and V
respectively are the height, curved surface area and the volume of a cone
Prove that 3pVh3 – c2 h2 + 9V2
= 0.
10. An agricultural field is in the form of a rectangle of
length 20m and width 14m. A pit 6m long, 3m wide and 2.5m deep is dug in the
corner of the field , and the earth taken out of the pit is spread uniformly
over the remaining area of the field . Find the extent to which the level of
the field has been raised. (17.18cm0
11. The cost of preparing the walls of the room 12m long at
the rate of Rs. 1.35 per m2 Is Rs.340.20 and the cost of
matting the floor
at 85paise / m2 is Rs.91.80. Find the height of the room. ( 6m)
12.To construct a wall 24m long, 0.4m thick and 6m high,
bricks of dimensions 25cm X 16cm X 10cm each are
used. If the
mortar occupies 1/ 10th of the volume of the wall,Find the number of bricks
used. ( 12960)
13.A well with 10m inside diameter is dug, 14m deep, earth
taken out of it and spread all around to width of 5m to
form an
embankment.Find the height of embankment.(4.66cm)
14.Water is flowing at the rate of 3km/hr. through a
circular pipe of 20 cm internal diameter into a circular cistern
of diameter 10m
and depth 2m. In how much time will this cistern will be filled? ( 1hr. 40 min.)
15.Water is flowing at the rate of 7m/s through a circular
pipe, whose internal diameter is 2cm
into a cylindrical
tank , the
radius of whose base is 40cm. Determine the increase in the water level in
1/2hrs. (787.5cm)
16. A sector of a circle of radius 12cm has the angle 120°. It
is rolled up so that to bounding radii are joined
together to form
a cone. Find the volume of the cone.(189.61cm3)
17. Water flows at the rate of 10m /min. through a
cylindrical pipe 5mm in diameter . How long would it take to fill
a conical vessel
whose diameter at the base is 40cm and depth 24cm? (51min.12sec)
18. A heap of wheat is in the form of a cone of diameter 9m
and height 3.5m find its volume, how much canvas
cloth is
required to just cover the heap. (Take p =
3.14) ( 74.25m3, 80.54m2 )
19. The radius of the internal and external surfaces of a
hollow spherical shell are 3cm and 5cm respectively. If it is
melted and
recast into a solid cylinder of height 22/3. Find the
diameter of the cylinder. ( 14cm)
20. A toy is in the form of a cone mounted on a hemi sphere
of radius 3.5 cm . If the total
height of the
toy is 15.5cm. Find volume of the toy.
(Take p
= 22/7) (
243.83cm)
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