Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Mensuration – III (Surface Area and Volume of a Right Circular Cylinder) Exercise 22.2
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Page 1
Use p = 22/7, unless otherwise indicated
1. Find the volume of a cylinder whose
(i) r = 3.5 cm, h = 40 cm
(ii) r = 2.8 m, h = 15 m
Solution:
(i) Given,
r = 3.5 cm
h = 40 cm
By using the formula,
Volume of a cylinder = pr
2
h
= 22/7 × 3.5 × 3.5 × 40
= 1540 cm
3
(ii) Given,
r = 2.8 m
h =15 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 2.8 × 2.8 × 15
= 369.6 m
3
2. Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h)
are:
(i) d = 21 cm, h = 10 cm
(ii) d = 7 m, h = 24 m
Solution:
(i) Given,
d = 21cm
r = d/2 = 21/2cm
h = 10 cm.
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 21/2 × 21/2 × 10
= 3465 cm
3
(ii) Given,
Page 2
Use p = 22/7, unless otherwise indicated
1. Find the volume of a cylinder whose
(i) r = 3.5 cm, h = 40 cm
(ii) r = 2.8 m, h = 15 m
Solution:
(i) Given,
r = 3.5 cm
h = 40 cm
By using the formula,
Volume of a cylinder = pr
2
h
= 22/7 × 3.5 × 3.5 × 40
= 1540 cm
3
(ii) Given,
r = 2.8 m
h =15 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 2.8 × 2.8 × 15
= 369.6 m
3
2. Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h)
are:
(i) d = 21 cm, h = 10 cm
(ii) d = 7 m, h = 24 m
Solution:
(i) Given,
d = 21cm
r = d/2 = 21/2cm
h = 10 cm.
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 21/2 × 21/2 × 10
= 3465 cm
3
(ii) Given,
d = 7 m
r = d/2 = 7/2m
h = 24 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 7/2 × 7/2 × 24
= 924 m
3
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 25 cm.
Find the volume of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 25 cm
Let the radius of cylinder be ‘r’ cm
By using the formula,
Area of base of right circular cylinder = pr
2
So,
pr
2
= 616
22/7 × r
2
= 616
r
2
= 616 × 7/22
= 196
r = v196
= 14cm
Volume of cylinder = Area of base of right circular cylinder × height
= 616 × 25
= 15400 cm
3
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
the volume of the cylinder.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
Let ‘r’ be the radius of the cylinder.
By using the formula,
Circumference of base of cylinder = 2pr
So,
Page 3
Use p = 22/7, unless otherwise indicated
1. Find the volume of a cylinder whose
(i) r = 3.5 cm, h = 40 cm
(ii) r = 2.8 m, h = 15 m
Solution:
(i) Given,
r = 3.5 cm
h = 40 cm
By using the formula,
Volume of a cylinder = pr
2
h
= 22/7 × 3.5 × 3.5 × 40
= 1540 cm
3
(ii) Given,
r = 2.8 m
h =15 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 2.8 × 2.8 × 15
= 369.6 m
3
2. Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h)
are:
(i) d = 21 cm, h = 10 cm
(ii) d = 7 m, h = 24 m
Solution:
(i) Given,
d = 21cm
r = d/2 = 21/2cm
h = 10 cm.
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 21/2 × 21/2 × 10
= 3465 cm
3
(ii) Given,
d = 7 m
r = d/2 = 7/2m
h = 24 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 7/2 × 7/2 × 24
= 924 m
3
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 25 cm.
Find the volume of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 25 cm
Let the radius of cylinder be ‘r’ cm
By using the formula,
Area of base of right circular cylinder = pr
2
So,
pr
2
= 616
22/7 × r
2
= 616
r
2
= 616 × 7/22
= 196
r = v196
= 14cm
Volume of cylinder = Area of base of right circular cylinder × height
= 616 × 25
= 15400 cm
3
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
the volume of the cylinder.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
Let ‘r’ be the radius of the cylinder.
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88 × 7 / 2 × 22
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Volume of cylinder = pr
2
h
= 22/7 × 14 × 14 × 15
= 9240 cm
3
5. A hollow cylindrical pipe is 21 dm long. Its outré and inner diameters are 10 cm
and 6 cm respectively. Find the volume of the copper used in making the pipe.
Solution:
We have,
Length of cylinder = 21 dm = 210 cm
Outer diameter = 10 cm
Outer radius, R = 10/2 = 5cm
Inner diameter = 6 cm
Inner radius, r = 6/2 = 3cm
? Volume of copper used in making the pipe = p (R
2
– r
2
)h
= 22/7 (5
2
- 3
2
) 210
= 22/7 (25-9) 210
= 10560 cm
3
6. Find the (i) curved surface area (ii) total surface area and (iii) volume of a right
circular cylinder whose height is 15 cm and the radius of the base is 7 cm.
Solution:
We have,
Height of cylinder = 15 cm
Radius of base = 7 cm
(i) Curved surface area = 2prh
= 2 × 22/7 × 7 × 15
= 660 cm
2
(ii) Total surface area = 2pr(h+r)
= 2 × 22/7 × 7 (15+7)
= 968 cm
2
(iii) Volume of cylinder = pr
2
h
Page 4
Use p = 22/7, unless otherwise indicated
1. Find the volume of a cylinder whose
(i) r = 3.5 cm, h = 40 cm
(ii) r = 2.8 m, h = 15 m
Solution:
(i) Given,
r = 3.5 cm
h = 40 cm
By using the formula,
Volume of a cylinder = pr
2
h
= 22/7 × 3.5 × 3.5 × 40
= 1540 cm
3
(ii) Given,
r = 2.8 m
h =15 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 2.8 × 2.8 × 15
= 369.6 m
3
2. Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h)
are:
(i) d = 21 cm, h = 10 cm
(ii) d = 7 m, h = 24 m
Solution:
(i) Given,
d = 21cm
r = d/2 = 21/2cm
h = 10 cm.
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 21/2 × 21/2 × 10
= 3465 cm
3
(ii) Given,
d = 7 m
r = d/2 = 7/2m
h = 24 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 7/2 × 7/2 × 24
= 924 m
3
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 25 cm.
Find the volume of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 25 cm
Let the radius of cylinder be ‘r’ cm
By using the formula,
Area of base of right circular cylinder = pr
2
So,
pr
2
= 616
22/7 × r
2
= 616
r
2
= 616 × 7/22
= 196
r = v196
= 14cm
Volume of cylinder = Area of base of right circular cylinder × height
= 616 × 25
= 15400 cm
3
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
the volume of the cylinder.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
Let ‘r’ be the radius of the cylinder.
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88 × 7 / 2 × 22
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Volume of cylinder = pr
2
h
= 22/7 × 14 × 14 × 15
= 9240 cm
3
5. A hollow cylindrical pipe is 21 dm long. Its outré and inner diameters are 10 cm
and 6 cm respectively. Find the volume of the copper used in making the pipe.
Solution:
We have,
Length of cylinder = 21 dm = 210 cm
Outer diameter = 10 cm
Outer radius, R = 10/2 = 5cm
Inner diameter = 6 cm
Inner radius, r = 6/2 = 3cm
? Volume of copper used in making the pipe = p (R
2
– r
2
)h
= 22/7 (5
2
- 3
2
) 210
= 22/7 (25-9) 210
= 10560 cm
3
6. Find the (i) curved surface area (ii) total surface area and (iii) volume of a right
circular cylinder whose height is 15 cm and the radius of the base is 7 cm.
Solution:
We have,
Height of cylinder = 15 cm
Radius of base = 7 cm
(i) Curved surface area = 2prh
= 2 × 22/7 × 7 × 15
= 660 cm
2
(ii) Total surface area = 2pr(h+r)
= 2 × 22/7 × 7 (15+7)
= 968 cm
2
(iii) Volume of cylinder = pr
2
h
= 22/7 × 7 × 7 × 15
= 2310 cm
3
7. The diameter of the base of a right circular cylinder is 42 cm and its height is 10
cm. Find the volume of the cylinder.
Solution:
We have,
Diameter of base of cylinder = 42 cm
Radius of base = d/2 = 42/2 = 21cm
Height = 10 cm
? Volume of cylinder = pr
2
h
= 22/7 × 21 × 21 × 10
= 13860 cm
3
8. Find the volume of cylinder, the diameter of whose base is 7 cm and height being
60 cm. Also, find the capacity of the cylinder in litres.
Solution:
We have,
Diameter of base = 7 cm
Radius of base = d/2 = 7/2 cm
Height of cylinder = 60 cm
Volume of cylinder = pr
2
h
= 22/7 × 7/2 × 7/2 × 60
= 2310 cm
3
Capacity of cylinder in litres = 2310 / 1000 = 2.31 litres.
9. A rectangular strip 25 cm× 7 cm is rotated about the longer side. Find the volume
of the solid, thus generated.
Solution:
Given,
Dimensions of rectangular strip = 25 cm × 7 cm
When it rotated about longer side it becomes,
Radius of base = 7 cm
Height of cylinder = 25 cm
Volume of cylinder = pr
2
h
= 22/7 × 7 × 7 × 25
= 3850 cm
3
10. A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its length to form a
Page 5
Use p = 22/7, unless otherwise indicated
1. Find the volume of a cylinder whose
(i) r = 3.5 cm, h = 40 cm
(ii) r = 2.8 m, h = 15 m
Solution:
(i) Given,
r = 3.5 cm
h = 40 cm
By using the formula,
Volume of a cylinder = pr
2
h
= 22/7 × 3.5 × 3.5 × 40
= 1540 cm
3
(ii) Given,
r = 2.8 m
h =15 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 2.8 × 2.8 × 15
= 369.6 m
3
2. Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h)
are:
(i) d = 21 cm, h = 10 cm
(ii) d = 7 m, h = 24 m
Solution:
(i) Given,
d = 21cm
r = d/2 = 21/2cm
h = 10 cm.
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 21/2 × 21/2 × 10
= 3465 cm
3
(ii) Given,
d = 7 m
r = d/2 = 7/2m
h = 24 m
By using the formula,
Volume of cylinder = pr
2
h
= 22/7 × 7/2 × 7/2 × 24
= 924 m
3
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 25 cm.
Find the volume of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 25 cm
Let the radius of cylinder be ‘r’ cm
By using the formula,
Area of base of right circular cylinder = pr
2
So,
pr
2
= 616
22/7 × r
2
= 616
r
2
= 616 × 7/22
= 196
r = v196
= 14cm
Volume of cylinder = Area of base of right circular cylinder × height
= 616 × 25
= 15400 cm
3
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
the volume of the cylinder.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
Let ‘r’ be the radius of the cylinder.
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88 × 7 / 2 × 22
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Volume of cylinder = pr
2
h
= 22/7 × 14 × 14 × 15
= 9240 cm
3
5. A hollow cylindrical pipe is 21 dm long. Its outré and inner diameters are 10 cm
and 6 cm respectively. Find the volume of the copper used in making the pipe.
Solution:
We have,
Length of cylinder = 21 dm = 210 cm
Outer diameter = 10 cm
Outer radius, R = 10/2 = 5cm
Inner diameter = 6 cm
Inner radius, r = 6/2 = 3cm
? Volume of copper used in making the pipe = p (R
2
– r
2
)h
= 22/7 (5
2
- 3
2
) 210
= 22/7 (25-9) 210
= 10560 cm
3
6. Find the (i) curved surface area (ii) total surface area and (iii) volume of a right
circular cylinder whose height is 15 cm and the radius of the base is 7 cm.
Solution:
We have,
Height of cylinder = 15 cm
Radius of base = 7 cm
(i) Curved surface area = 2prh
= 2 × 22/7 × 7 × 15
= 660 cm
2
(ii) Total surface area = 2pr(h+r)
= 2 × 22/7 × 7 (15+7)
= 968 cm
2
(iii) Volume of cylinder = pr
2
h
= 22/7 × 7 × 7 × 15
= 2310 cm
3
7. The diameter of the base of a right circular cylinder is 42 cm and its height is 10
cm. Find the volume of the cylinder.
Solution:
We have,
Diameter of base of cylinder = 42 cm
Radius of base = d/2 = 42/2 = 21cm
Height = 10 cm
? Volume of cylinder = pr
2
h
= 22/7 × 21 × 21 × 10
= 13860 cm
3
8. Find the volume of cylinder, the diameter of whose base is 7 cm and height being
60 cm. Also, find the capacity of the cylinder in litres.
Solution:
We have,
Diameter of base = 7 cm
Radius of base = d/2 = 7/2 cm
Height of cylinder = 60 cm
Volume of cylinder = pr
2
h
= 22/7 × 7/2 × 7/2 × 60
= 2310 cm
3
Capacity of cylinder in litres = 2310 / 1000 = 2.31 litres.
9. A rectangular strip 25 cm× 7 cm is rotated about the longer side. Find the volume
of the solid, thus generated.
Solution:
Given,
Dimensions of rectangular strip = 25 cm × 7 cm
When it rotated about longer side it becomes,
Radius of base = 7 cm
Height of cylinder = 25 cm
Volume of cylinder = pr
2
h
= 22/7 × 7 × 7 × 25
= 3850 cm
3
10. A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its length to form a
cylinder. Find the volume of the cylinder so formed.
Solution:
We have,
Dimensions of rectangular sheet = 44cm × 20cm
When it rolled along its length it becomes,
Radius of base = length/2p
= 44×7 / 2×22
= 7cm
Height of cylinder = 20 cm
? Volume of cylinder = pr
2
h
= 22/7 × 7 × 7 × 20
= 3080 cm
3
11. The volume and the curved surface area of cylinder are 1650 cm
3
and 660
cm
2
respectively. Find the radius and height of the cylinder.
Solution:
We have,
Volume of cylinder = 1650 cm
3
Curved surface area = 660 cm
2
Volume of cylinder/curved surface area = 1650/660
pr
2
h/ 2prh = 1650/660
r/ 2 = 5/2
r = 5cm
Surface area = 660 cm
2
2prh = 660
2 × 22/7 × 5 × h = 660
h = 660×7 / 2×22×5
= 4620/220
= 21cm
? Radius = 5cm and height = 21cm
12. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio
5:3. Calculate the ratio of their volumes.
Solution:
We have,
Ratio of radii of two cylinder = 2:3
Radius of cylinder 1 = r
1
Radius of cylinder 2 = r
2
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