9th Maths 13.5
Chapter 13
Surface Areas and Volumes
NCERT Class 9th solution of Exercise 13.1
NCERT Class 9th solution of Exercise 13.2
NCERT Class 9th solution of Exercise 13.3
NCERT Class 9th solution of Exercise 13.4
NCERT Class 9th solution of Exercise 13.6
NCERT Class 9th solution of Exercise 13.7
NCERT Class 9th solution of Exercise 13.8
Exercise 13.5
Q1. A matchbox measures 4cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes?
Sol. :
Given:
Length of Matchbox l=4cm
The breadth of Matchbox b=2.5cm
The Height of Matchbox h=1.5cm
To Find:
The volume of a packet.
Solve:
The volume of a Matchbox =l×b×h
=4×2.5×1.5cm
=15cm3
The volume of a Packet = Volume of 12 Matchbox
=12×15
=180cm3
Answer:
The volume of a Packet is 180cm3.
Q2. A cuboical water tank is 6m long, 5m wide and 4.5m deep. How many litres of water can it hold?(1m3=1000l)
Sol. :
Given:
Length of Tank =6m
Breadth of Tank =5m
Height of Tank =4.5m
To Find:
Amount of water in the tank.
Solve:
Volume of Tank =l×b×h
=6×5×4.5
=135m3
=135×1000l [1m3=1000l]
=135000l
Answer:
Amount of water in the tank 135000l.
Q3. A cuboidal vessel is 10m long and 8m wide. How high must it be made to hold 380 cubic metres of liquid?
Sol. ;
Given:
The Length of Vessel l=10m
The breadth of Vessel b=8m
Volume of Vessel =380m3
To Find:
Height of Vessel h.
Solve:
Volume of Vessel =l×b×h
380=10×8×h
h=38010×8
h=4.75m
Answer:
Height of the Vessel h=4.75m.
Q4. Find the cost of digging a cuboidal pit 8m long, 6m broad and 3m deep at the rate of ₹30perm3.
Sol. :
Given:
The Length of Pit l=8m
The breadth of Pit b=6m
The Height of pit h=3m
Rate ₹30 per m3
To Find:
Cost of digging.
Solve:
Volume of Pit =l×b×l
=8×6×3
=144m3
Cost of digging = Volume × Rate
=₹144×30
=₹4320
Answer:
Cost of digging ₹4320.
Q5. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5m and 10m.
Sol. :
Given:
Volume of tank is 50000 litres =500001000m3 [1m3=1000litres]
=50m3
The length of the tank is l=2.5m
The height of the tank is h=10m
To Find:
Breadth b.
Solve:
Volume of tank =l×b×h
50=2.5×breadth×10
breadth =502.4×10)
breadth =2m
Answer:
The breadth of the Tank is 2m.
Q6. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20m×15m×6m. For how many days will the water of this tank last?
Sol. :
Given:
The length of tank is l=20m
The breadth of tank is b=15m
The height of the tank is h=6m
The population of the village is 4000
Water per day per head =150
To find:
The water will last in a number of days.
Solve:
Number of days = (Volume of tank)/(Total water per day per head)
Number of days =l×b×h4000×150
=20×15×64000×150
=3 Days
Answer:
The water will last in 3 days.
Q7. A godown measures 40m×25m×15m. Find the maximum number of wooden crates each measuring 1.25m×1.25m×0.5m that can be stored in the godown.
Sol. :
Given:
Volume of godown =40m times 25m times 15`
Volume of crate =1.25×1.25×0.5
To Find :
Number of crates can store in godown.
Solve:
Number of crates in godown = (Volume of godown)/(Volume of a creat.)
=40×25×151.25×1.25×0.5.
=16000
Answer:
16000 crates can store in godown.
Q8. A solid cube of side 12cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Sol. :
Given:
Side of Old Cube is 12cm.
Number of New Cubes are 8.
To Find:
Ratio of their Surface Area.
Solve:
Volume of Old Cube =(Side)3=(12)3
Side of New Cube =18×VolumeofOld
=18×(12)3
=6cm
Ratio of their Surface area =6(side)26(side)2
=12×126×6
=41=4:1
Answer:
Ratio of their Surface Area 4:1
Q9. A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?
Sol. :
Given:
Height of river h=3m
Breadth of ever b=40m
Length of river l=2km per hour =200060meter per minute.
To Find:
Volume of Water fall into the sea in a minute.
Solve:
Volume of Water fall into the sea in a minute
=(l×b×h)
=2000×40×360
=4000m3
Answer:
Volume of Water fall into the sea in a minute 4000m3.
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