1. The length, breadth and height of a water tank are 5.0 m, 2.5 metre and 1.25 metre respectively .calculate the capacity of the water tank in a) m³ b)Litre
Ans. Dimensions of of a water tank is given as length=5.0m , breadth=2.5m height=1.25m
V=l×b×h
V=5.0m×2.5m×1.25m
=15.625m³
Once again ,
V=5×100 cm ×2.5×100×1.25×100cm (1m=100cm)
=500cm×250cm×125cm
=15625000cm³
=15625×1000cm³
=15625 ×1L (1000cm³= 1L)
=15625L.
2. A solid silver piece is immersed in water contained in a measuring cylinder .the level of water rises from 50 ml to 62 ml .find the volume of silver piece?
Ans. Liquid displacement method for finding volume of a solid body is used.
V1=50 ml ,V2=62ml
V=V2 -V1
V=62ml -50ml
=12ml
=12× 1ml
=12×1cm³ (1ml=1cm³)
=12cm³.
3. Find the volume of a liquid present in a disc of dimensions 10 cm×10cm×5cm?
Ans. Dimension given means l=10cm, b=10cm, & h=5cm.
V=l×b×h
V=10cm×10cm×5cm
=500cm³
=500×1cm³
=500mL (1cm³=1mL)
4. A rectangular field is of length 60 m and breadth 35m . find the area of the field?
Ans.l=60m, b=35m
A=l×b
A=60m×35m
=2100m²
5. Find the approximate area of an irregular lamina of which boundary line is drawn on the graph paper shown in figure 1.16 below.
Ans. Graphical method of finding area of a an irregular lamina is to be used.
A=No. of complete boxes + No. of half boxes and more than half .
A=10 complete boxes + 11 more than half boxes
=21 boxes
=21×1 box
=21 cm². (Area of 1 box=1cm²)
6.A piece of brass of volume 30 cm³ has a mass of 252 gram. find the density of brass in a)gcm³. b)kgm³
Ans. Given,
V=30cm³, M=252g
Density= M/V
Density= 252g/30cm³
=8.4 gcm-³
In terms of SI unit of density,
Density=8.4× 1 gcm-³
=8.4× 1000kgm-³. (1gcm-³=1000kgm-³)
= 8400 kgm-³
7. The the mass of an iron ball is 312 gram. The density of iron is 7.8 gram per centimetre cube. Find the volume of the ball?
Ans. Given ,
M=312g. Density=7.8gcm-³
Density=mass/volume.
Density×volume=mass
volume=mass/density
= 312 g/7.8 gcm-³
=40 cm³.
8. A cork has a volume 25 cm-³. The density of crop is 0.25 gram per centimetre cube. Find the mass of the cork?
Ans. Given,
Volume=25cm-³.
Density=0.25gcm-³
Mass=?
Density=mass/volume
Density×volume=mass
Mass=density×volume
Mass=0.25 gcm-³ × 25 cm³
=6.25 g.
9. The mass of 5 litre of water is 5 kg.find the density of water in gram per centimetre cube?
Ans. Given,
Mass=5.0 kg
=5.0× 1.0 kg
=5.0 × 1000g. (1 kg=1000g)
=5000 g.
Volume=5.0 L
=5.0 × 1L
= 5.0 × 1000cm³. (1L=1000cm³)
=5000 cm³
Density=mass/volume.
Density=5000g/5000cm³
=1 gcm-³.
10. A cubical tank of side 1m field with 800 kg of a liquid. Find: a) the volume of tank b) the density of liquid in kgm-³.
Ans. Given,
Cube of side 1 metre.
Volume of a cube=s×s×s
Volume=1m×1m×1m
= 1m³.
Density=mass/volume.
Density=800kg/1m³
=800 kgm-³.
11. A block of iron has dimensions 2m×0.5 m×0.25m. the density of iron is 7.8 gcm-³. Find the mass of block?
Ans. Given,
Dimensions as l=2.0m, b=0.5m & h=0.25m
V=l×b×h
V=2.0m×0.5m×0.25m
=0.25m-³
Density=7.8 gcm-³
=7.8× 1 gcm-³
=7.8× 1000 kgm-³
=7800 kgm-³
Mass=?
Density=mass/volume.
Density×volume=mass
Mass=density×volume
= 7800 kgm-³ × 0.25 m-³
=1950kg.
12. The mass of a lead piece is 115 g. When it is immersed into a measuring cylinder, the water level rises from 20 ml mark to 30ml mark. Find
a) the volume of lead piece,
b) the density of the lead in kgm-³.
Ans. given,
Mass=115 g.
Volume to be calculated by liquid displacement method.
V2=30 mL. , V1=20 mL
V =V2 - V1
V=30mL - 20 mL
=10 mL.
=10×1mL
=10 × 1cm³. (1mL=1cm³)
= 10 cm³
Density=mass/volume.
Density=115 g/10 cm³
=11.5 gcm-³
=11.5 × 1 gcm-³
=11.5 × 1000 kgm-³. (1gcm-³= 1000 kgm-³)
=11500 kgm-³.
13. The density of copper is 8.9 g cm-3. What will be its density in kgm-³?
Ans. Density of copper is 8.9gcm-³
In S.I unit density of copper=8.9× 1 gcm-³
=8.9×1000kgm-³ (1gcm-³=1000 kgm-³)
=8900 kgm-³.
14. A car travels a distance of 15 kilometre in 20 minutes find the speed of the car in a) kmh-¹ b)ms-¹
Ans. Distance travelled=15 km
Time taken=20 minutes
=20× 1 minute
=20×1/60 h. (1hour=60 minutes,
1h=60×1 minutes, 1/60 h =1 minute)
=1/3 h
Speed=distance travelled/time taken
Speed=25 km / 1/3 h
=45 kmh-¹.
But ,
Speed=45 kmh-¹
=45× 1 kmh-¹
=45× 5/18 ms-¹
=12.5 ms-¹.
15. How long a train will take to travel a distance of 200 kilo metre with a speed of 60 kilometre per hour?
Ans. Given,
Distance travelled=200 km.
Speed=60 kmh-¹
Time taken=?
Speed=distance travelled/time taken
Speed×time taken=distance travel
Time taken=Distance travelled/speed
=200km/60 kmh-¹
=20/6 h
=3h + 2/6 h
=3h + 2/6 × 1h
= 3 h + 2/6 × 60 minutes. (1hour = 60 minutes)
= 3h + 2×10 minutes
= 3h + 20 minutes
=3h 20 minutes.
16. A boy travels with a speed of 10 ms-¹ for 30 minute. How much distance does he travel?
Ans. given,
Speed=10 ms-¹
Time=30 minutes
=30× 1 minute
=30× 60 s. (1 minute =60s)
= 1800 s
Distance travelled=?
Speed=distance travelled/time taken
Speed×time taken=distance travelled
distance travelled=speed×time taken
=10ms-¹ × 1800 s
=1800m
=1800×1m
=1800×1/1000 km. (1km=1000m, 1km=1000× 1m , 1/1000 km = 1 m)
=1.8 km.
17. Express 36 kmh-¹ in ms-¹.
Ans. 36 km/h = 36×1 km/h. (1km=1000m,1h=60×60s)
=36 ×1000 m / 60×60 s
=36 ×5/18 ms-¹
=2×5 ms-¹
=10 ms-¹.
18. Express 15 ms-¹ in kmh-¹
Ans.15 ms-¹ =15×1ms-¹
= 15× 18/5 kmh-¹. (1ms-¹=18/5 kmh-¹)
=3×18 kmh-¹
= 54 kmh-¹.
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