9th Maths 13.7
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 13.6
NCERT Class 9th solution of Exercise 13.8
Exercise 13.7
Assume π=227, unless stated otherwise.
Q1. Find the volume of the right circular cone with
i) radius 6cm, height 7cm ii) radius 3.5cm, heirht 12cm
Sol.
i)
Volume of the right circular cone =13πr2h
=13×227×(6)2×7
=264cm3
Answer:
Volume of the right circular cone 264cm2.
ii)
Volume of the right circular cone =13πr2h
=13×227×(3.5)2×12
=154cm3
Answer:
Volume of the right circular cone 154cm3.
Q2. Find the capacity in litres of a conical vessel with
i) radius 7cm slant height 25cm ii) height 12cm, slant height 13cm.
Sol. :
i)
Height of the cone h=√l2-r2
=√(25)2-(7)2
=√625-49
=√576
=24
Volume of the conical vessel =13πr2h
=13×227×(7)2×24
=1232cm3
=(12321000)l
=1.232l
Answer:
The capacity of the conical vessel 1.232l.
ii)
Radius of cone r=√l2-h2
r=√(13)2-(12)2
r=√169-144
r=√25
r=5cm
Volume of the conical vessel =13πr2h
=13×227×(5)2×12
=22007cm3
Capacity of the conical vessel in litres
=22007×11000=1135l
Answer:
Capacity of the conical vessel 1135l.
Q3. The height of a cone is 15cm. If its volume is 1570cm3, find the radius of the base.
(Use π=3.14)
Sol. :
Given:
Height of a cone h=15cm
Volume of cone =1570cm3
To Find:
The radius of the base.
solve:
Volume of cone =13πr2h
1570=13×3.14r2×15
r2=1570×33.14×15
r2=100
r=10cm
Answer:
The radius of the base 10cm.
Q4. If the volume of a right circular cone of height 9cm is 48πcm3, find the diameter of its base.
Sol. :
Given:
Height of cone h=9cm
Volume of cone =48πcm3
To Find:
The diameter of base.
Solve:
Volume of the cone =13πr2h
48π=13πr2×9
r2=48π×39π
r2=16
r=4cm
Daimeter =2×4=8cm
Answer:
The diameter of the base of the cone 8cm.
Q5. A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kilolitres?
Sol. :
Given:
Radius of conical pit r=3.52m
Height of conical pit h=12m
To Find:
Capacity of conical pit in kilolitres.
Solve:
Volume of conical pit =13πr2h
=13×227×(3.52)2×12
=38.5m3
Capacity of conical pit =38.5 kilolitres.
Answer:
Capacity of conical pit 38.5 kilolitres.
Q6. The volume of a right circular cone is 9856cm3. If the diameter of the base is 28cm,
find
i) height of the cone ii) slant height of the cone
iii) curved surface area of the cone.
Sol. :
Given:
The volume of cone 9856cm3
The radius of the base r=282=14cm
To find:
i) height of the cone
ii) slant height of the cone
iii) curved surface area of the cone.
Solve:
i) Volume of cone =13πr2h
9856=13×227×(14)2×h
h=9856×3×722×14×14
h=48cm
Answer:
height of the cone 48cm
ii) Slant height of the cone l=√h2+r2
l=√(48)2+(14)2
l=√2304+196
l=√2500
l=50cm
Answer:
Slant height of the cone 50cm.
iii) curved surface area of cone =πrl
=227×14×50
=2200cm2
Answer:
Curved surface area of cone 2200cm2.
Q7. A right triangle ABC with sides 5cm,12cm, and 13cm is revolved about the side 12cm. Find the volume of the solid so obtained.
Sol. :
Given:
Radius r=5cm
Height h=12cm
To Find:
Volume of the solid.
Solve:
Volume of cone =13πr2h
=13×π×(5)2×12
=100πcm3
Answer:
Volume of solid 100πcm3.
Q8. If the triangle ABC in the Question 7 above is revolved about the side 5cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Question 7 and 8.
Sol. :
Given:
Radius r=12cm
Height h=5
To Find:
Volume of the solid.
Solve:
Volume of cone =13πr2h
=13×227×(12)2×5
=240πcm3.
Ratio of the volume of Question 7 and 8
=100π:240π
=5:12
Answer:
Volume of cone 240π, and Ratio 5:12.
Q9. A heap of wheat is in the form of a cone whose diameter is 10.5m and height is 3m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Sol. :
Given:
Radius of cone r=10.52=5.25m
Height of cone h=3m
To Find:
The area of the canvas.
Solve:
Volume of cone =13πr2h
=13×227×(5.25)2×3
=86.625m3
Slant height l=h2+r2
l2=(3)2+(5.25)2
l2=9+27.5625
l=√36.5625=6.0467 (approx)
The area of the canvas = Curved surface area of cone
=πrl
=227×5.25×6.0467
=99.77m2 (approx)
Answer:
The area of the canvas is 99.77m2.
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