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 `4cmtimes2.5cmtimes1.5cm.` 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 timesbtimesh`
`=4times2.5times1.5cm`
`=15cm^3`
The volume of a Packet = Volume of `12` Matchbox
`=12times15`
`=180cm^3`
Answer:
The volume of a Packet is `180cm^3`.
Q2. A cuboical water tank is `6m` long, `5m` wide and `4.5m` deep. How many litres of water can it hold?(`1m^3=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 timesbtimesh`
`=6times5times4.5`
`=135m^3`
`=135times1000l` [`1 m^3 = 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 `=380m^3`
To Find:
Height of Vessel `h`.
Solve:
Volume of Vessel `=l times b times h`
`380 = 10 times 8 times h`
`h = 380/(10 times 8)`
`h = 4.75 m`
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 `₹30`per`m^3`.
Sol. :
Given:
The Length of Pit `l=8m`
The breadth of Pit `b=6m`
The Height of pit `h=3m`
Rate `₹30` per `m^3`
To Find:
Cost of digging.
Solve:
Volume of Pit `=l times b times l`
`=8 times 6 times 3`
`=144 m^3`
Cost of digging = Volume `times` Rate
`=₹144 times 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 `=(50000)/1000m^3` [`1m^3 = 1000`litres]
`= 50 m^3`
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 times b times h`
`50 = 2.5 times breadth times 10`
breadth `= (50)/(2.4 times 10`)
breadth `= 2 m`
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 `20mtimes15mtimes6m`. 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 times b times h)/(4000 times 150)`
`=(20 times 15 times 6)/(4000 times 150)`
`=3` Days
Answer:
The water will last in 3 days.
Q7. A godown measures `40mtimes25mtimes15m`. Find the maximum number of wooden crates each measuring `1.25mtimes1.25mtimes0.5m` that can be stored in the godown.
Sol. :
Given:
Volume of godown `=`40m times 25m times 15`
Volume of crate `=1.25 times 1.25 times 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 times 25 times 15)/(1.25 times 1.25 times 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 `=1/8times Volume of Old`
`=1/8times(12)^3`
`=6cm`
Ratio of their Surface area `= (6(side)^2)/(6(side)^2`
`=(12 times 12)/(6 times 6)`
`=4/1= 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 `=2000/60`meter 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 times b times h)`
`=(2000 times 40 times 3)/(60)`
`=4000m^3`
Answer:
Volume of Water fall into the sea in a minute `4000m^3`.
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