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Published on: 03/10/2019
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1.
Three horses are tethered at 3 corner of a triangular plot having sides 20 m, 30 m and 40 m with ropes of 7 m length each. Find the area of this plot which can be grazed by the horses.
2.
The length of a certain sector of a circle of radius 5.6 cm is 17.2 cm. Find the area of the sector.
3.
Find the area of an annulus whose inner and outer radii are :
(i) 12 cm and 16 cm
(ii) 6 cm and 8 cm
(iii) 3 cm and 4 cm.
4.
A bicycle wheel whose diameter is 77 cm makes 50 revolutions in 20 seconds. Find the speed in km/h.
5.
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 am and 6 : 40 am.
6.
A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road.
7.
A bus has wheels which are 112 cm in diameter. How many complete revolutions does each wheel make in 20 minutes, when the bus is travelling at a speed of 66 km/h?
8.
The long and short hands of a clock are 6 cm and 3 cm respectively. Find the sum of distance travelled by their tips in a day.
9.
In fig., PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flowers beds (shaped parts).
10.
A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. If bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s, then calculate the number of complete revolutions the wheel makes in raising the bucket.
1.
77 m2
2.
16.8 cm2
3.
(i) 352 cm2 (ii) 88 cm2 (iii) 22 cm2
4.
21.8 km/h
5.
\(45\frac { 5 }{ 6 } { cm }^{ 2 }\)
6.
2618 m2
7.
6250
8.
\(\frac{6600}{7} cm\)
9.
Here PR2 = PQ2 + QR2
⇒ PR2 = (42)2 + (42)2
⇒PR=42√2m
⇒\(PO={42\sqrt2\over 2}=21\sqrt2m\)
Area of sector
\(={90^0\over 360^0}\times\pi(21\sqrt2)^2\)
\(={1\over4}\times{22\over 7}\times21\times21\times2\)
=693m2
Area of ΔPOS
\(={1\over 1}PO\times OS(∵ \ PO⊥OS)\)
\(={1\over 1}\times 21\sqrt2\times21\sqrt2=441m^2\)
∴ Area of one flower bed
=693-441=252m2
⇒ Area of two flower beds
=2 x 252 = 504m2
10.
Speed = 1.1m/s.
Time = 1 minute 28 second
= (60 + 28) sec = 88 sec
∴ Distance covered = 88 X 1.1 = 96.8 m.
∴ Length of rope = 96.8 m
Radius of wheel =\({77\over 2}cm\)
∴ Circumference of wheel
\(=2\times{22\over 7}\times{77\over 2}=242cm=2.42m\)
∴ No. of revolutions=\({96.8\over 2.42}=40\)
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