9th Maths 13.6
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 13.5
NCERT Class 9th solution of Exercise 13.7
NCERT Class 9th solution of Exercise 13.8
Exercise 13.6
Assume π=227, unless stated otherwise.
Q1. The circumference of the base of a cylindrical vessel is 132cm and its height is 25cm. How many litres of water can it hold?(1000cm3=1l)
Sol. :
Given:
Circumference of Base =132cm
Height of Cylinder h=25cm
To find:
Amount of water vessel can hold.
Solve:
Circumference of Base =2πr
132=2×227×r
r=132×722×2
r=21cm
Volume of Cylinder =πr2h
=227(21)2×25
=34650cm3
Amount of water vessel can hold
=(346501000) [1000cm3=1l]
=34.65 litres
Answer:
The vessel can hold 34.65 litres of water.
Q2. The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28cm. The length of the pipe is 35cm. Find the mass of pipe, if 1cm3 of wood has a mass of 0.6g.
Sol. :
Given:
Inner Radius of Cylinder r=242=12cm
Outer Radius of Cylinder R=282=14cm
Length of Cylinder h=35cm
Rate 0.6g per 1cm3
To Find:
The mass of pipe.
Solve:
Volume of the wooden pipe
= Volume of the external Cylinder - Volume of the Internal Cylinder
=πR2h-πr2h
=πh(R2-r2)
=227×35((14)2-(12)2)
=22×5(196-144)
=110×52
=5720cm3
Mass of the pipe = Volume×Rate
=5720×0.6g
=(343.21000)kg [1kg=11000g]
=3.432kg
Answer:
The Mass of pipe 3.432kg.
Q3. A soft drink is available in two packs - i) a tin can with a rectangular base of length 5cm and width 4cm, having a height of 15cm and ii) a plastic cylinder with circular base of diameter 7cm and height 10cm. Which container has greater capacity and by how much?
Sol. :
Given:
Length of tin can l=5cm
Breadth of tin can b=4cm
Height of tin can h=15cm
Radius of plastic cylinder r=72cm
Height of plastic cylinder h=10cm
To Find:
Capacity of tin can and plastic Cylinder.
Solve:
Capacity of tin can =l×b×h
=5×4×15
=300cm2
Capacity of plastic Cylinder =πr2h
=227(72)2×10
=385cm3
Differnce = Capacity of plastic cylinder - Capacity of tin can
=385-300=85cm3
Answer:
The plastic cylinder has greater capacity by 85cm3.
Q4. If the lateral surface of a cylinder is 94.2cm2 and its height is 5cm, then find
i) radius of its base ii) its volume. (Use π=3.14)
Sol, :
Given:
Lateral Surface of a Cylinder 94.2cm2
Height of a Cylinder 5cm
To Find:
i) radius of its base
ii) its volume
Solve:
i) Lateral Surface of a Cylinder =2πrh
94.2=2×3.14×r×5
r=94.22×3.14×5
r=3cm
Answer:
Radius of Cylinder 3cm.
ii) Volume of Cylinder =πr2h
=3.14(3)2×5
=141.3cm3
Answer:
Volume of Cylinder 141.3cm3.
Q5. It costs ₹2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of ₹20 per m2, find
i) inner curved surface area of the vessel,
ii) radius of the base,
iii) capacity of the vessel.
Sol. :
Given:
Total Cost of Paint ₹2200
Height of Cylinder h=10m
Rate of Paint ₹20 perm2
To Find:
i) inner curved surface area of the vessel,
ii) radius of the base,
iii) capacity of the vessel.
Solve:
i) Inner Curved Surface Area of the vessel = (Total cost of paint)/(Rate of paint)
=(220020)=110m2
Answer:
Inner Curved surface Area of the vessel 110m2.
ii) Curved Surface Area of Cylinder =2πrh
110=2227×r×10
r=110×72×22×10
r=74m
Answer:
Radius of base 74m
iii) Capacity of vessel =πr2h
=227×74×74×10
=96.25m3
Answer:
Capacity of vessel 96.25m3.
Q6. The capacity of a closed cylindrical vessel of height 1m is 15.4litres. How many square meters of metres of metal sheet would be needed to make it?
Sol. :
Given:
Capacity of closed Cylinder 15.4litres=(15.41000)=0.0154m3
Height of Cylinder h=1m
To Find:
Area of metal sheet.
Solve:
Volume of closed Cylinder =πr2h
0.0154=227×r2×1
r2=0.0154×722=0.0049
r=√0.0049
r=0.07
Area of Metal sheet =2πrh+2πr2
=2πr(h+r)
=2227×0.07(1+0.07)
=0.4708m2
Answer:
Area of metal sheet needed to make the vessel 0.4708m2.
Q7. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencils 7mm and the diameter of the graphite is 1mm. If the length of the pencil is 14cm, find the volume of the wood and that of the graphite.
Sol. :
Given:
Radius of graphit cylinder 12mm=120cm
Radius of pencil R=72mm=720cm
Height of the pencil h=14cm
To Find:
Volume of the wood and graphit.
Solve:
Volume of graphit cylinder =πr2h
=(227×(120)2×14)
=0.11cm3
Volume of the pencil=πR2h
=(227×(720)2×14)
=5.39cm3
Volume of wood = Volume of pencil - Volume of graphit
=5.39-0.11
=5.28cm3.
Answer:
Volume of wood 5.39cm3.
Q8. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7cm. If the bowl is filled with soup to a height of 4cm, how much soup the hospital has to prepare daily to serve 250 patients?
Sol. :
Given:
Radius of Bowl r=72cm
Height of Bowl h=4cm
To Find:
Volume of soup.
Solve:
Volume of Bowl =πr2h
=(227×(72)2×4)
=1.54cm3
Volume of soup =VolumeofaBowltimes 250`
=1.54×250
=38500cm3=38.5litres
Answer:
Volume of Soup 38.5litres.
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