Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Mensuration – III (Surface Area and Volume of a Right Circular Cylinder) Exercise 22.1
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Page 1
1. Find the curved surface area and total surface area of a cylinder, the diameter of
whose base is 7 cm and height is 60 cm.
Solution:
We have,
Diameter of cylinder = 7 cm
So, Radius of cylinder = 7/2 cm
Height of cylinder = 60 cm
By using the formula,
Curved surface area of cylinder = 2prh
= 2 × 22/7 × 7/2 × 60
= 1320 cm
2
Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7/2 (60 + 7/2)
= 22 (127/2)
= 1397 cm
2
2. The curved surface area of a cylindrical road is 132 cm
2
. Find its length if the
radius is 0.35 cm.
Solution:
We have,
Curved surface area of cylindrical road =132 cm
2
Radius of road = 0.35 cm
Let length of road be ‘h’ cm
By using the formula,
Curved surface area of cylindrical road = 2prh
So, 2prh = 132
2 × 22/7 × 0.35 × h = 132
h = 132×7 / 2×22×0.35
= 924 / 15.4
= 60cm
? Length of road is 60 cm.
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 2.5 cm.
Find the curved surface area of the cylinder.
Solution:
We have,
Page 2
1. Find the curved surface area and total surface area of a cylinder, the diameter of
whose base is 7 cm and height is 60 cm.
Solution:
We have,
Diameter of cylinder = 7 cm
So, Radius of cylinder = 7/2 cm
Height of cylinder = 60 cm
By using the formula,
Curved surface area of cylinder = 2prh
= 2 × 22/7 × 7/2 × 60
= 1320 cm
2
Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7/2 (60 + 7/2)
= 22 (127/2)
= 1397 cm
2
2. The curved surface area of a cylindrical road is 132 cm
2
. Find its length if the
radius is 0.35 cm.
Solution:
We have,
Curved surface area of cylindrical road =132 cm
2
Radius of road = 0.35 cm
Let length of road be ‘h’ cm
By using the formula,
Curved surface area of cylindrical road = 2prh
So, 2prh = 132
2 × 22/7 × 0.35 × h = 132
h = 132×7 / 2×22×0.35
= 924 / 15.4
= 60cm
? Length of road is 60 cm.
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 2.5 cm.
Find the curved surface area of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 2.5 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
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 2.5
= 1540/7
= 220 cm
2
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
its curved surface area and total surface area.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88×7 / 44
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 15
= 1320 cm
2
? Total surface area area of cylinder = 2pr (h+r)
= 2 × 22/7 × 14 (15 + 14)
= 2 × 22/7 × 14 × 29
= 2552 cm
2
Page 3
1. Find the curved surface area and total surface area of a cylinder, the diameter of
whose base is 7 cm and height is 60 cm.
Solution:
We have,
Diameter of cylinder = 7 cm
So, Radius of cylinder = 7/2 cm
Height of cylinder = 60 cm
By using the formula,
Curved surface area of cylinder = 2prh
= 2 × 22/7 × 7/2 × 60
= 1320 cm
2
Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7/2 (60 + 7/2)
= 22 (127/2)
= 1397 cm
2
2. The curved surface area of a cylindrical road is 132 cm
2
. Find its length if the
radius is 0.35 cm.
Solution:
We have,
Curved surface area of cylindrical road =132 cm
2
Radius of road = 0.35 cm
Let length of road be ‘h’ cm
By using the formula,
Curved surface area of cylindrical road = 2prh
So, 2prh = 132
2 × 22/7 × 0.35 × h = 132
h = 132×7 / 2×22×0.35
= 924 / 15.4
= 60cm
? Length of road is 60 cm.
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 2.5 cm.
Find the curved surface area of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 2.5 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
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 2.5
= 1540/7
= 220 cm
2
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
its curved surface area and total surface area.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88×7 / 44
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 15
= 1320 cm
2
? Total surface area area of cylinder = 2pr (h+r)
= 2 × 22/7 × 14 (15 + 14)
= 2 × 22/7 × 14 × 29
= 2552 cm
2
5. A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find the total
surface area of the solid thus generated.
Solution:
We have,
Dimension of rectangular strip = 25 cm × 7cm
When this strip is rotated about its longer side,
Height of cylinder becomes = 25 cm
Radius = 7 cm
? Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7 (25 + 7)
= 2 × 22/7 × 7 × 32
= 1408 cm
2
6. A rectangular sheet of paper, 44 cm× 20 cm, is rolled along its length to form a
cylinder. Find the total surface area of the cylinder thus generated.
Solution:
We have,
Dimensions of rectangular sheet of paper = 44cm × 20cm
When this sheet of paper is rolled along its length,
Circumference of base becomes = 44 cm
By using the formula,
Circumference of base = 2pr
So, 2pr = 44
2 × 22/7 × r = 44
r = 44×7 / 44
= 7cm
Radius = 7cm
Height = 20cm
? Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7 (20 + 7)
= 2 × 22/7 × 7 × 27
= 1188 cm
2
7. 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 curved surface areas.
Solution:
We have,
Ratio of radius of two cylinder, r
1
:r
2
= 2:3
Page 4
1. Find the curved surface area and total surface area of a cylinder, the diameter of
whose base is 7 cm and height is 60 cm.
Solution:
We have,
Diameter of cylinder = 7 cm
So, Radius of cylinder = 7/2 cm
Height of cylinder = 60 cm
By using the formula,
Curved surface area of cylinder = 2prh
= 2 × 22/7 × 7/2 × 60
= 1320 cm
2
Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7/2 (60 + 7/2)
= 22 (127/2)
= 1397 cm
2
2. The curved surface area of a cylindrical road is 132 cm
2
. Find its length if the
radius is 0.35 cm.
Solution:
We have,
Curved surface area of cylindrical road =132 cm
2
Radius of road = 0.35 cm
Let length of road be ‘h’ cm
By using the formula,
Curved surface area of cylindrical road = 2prh
So, 2prh = 132
2 × 22/7 × 0.35 × h = 132
h = 132×7 / 2×22×0.35
= 924 / 15.4
= 60cm
? Length of road is 60 cm.
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 2.5 cm.
Find the curved surface area of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 2.5 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
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 2.5
= 1540/7
= 220 cm
2
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
its curved surface area and total surface area.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88×7 / 44
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 15
= 1320 cm
2
? Total surface area area of cylinder = 2pr (h+r)
= 2 × 22/7 × 14 (15 + 14)
= 2 × 22/7 × 14 × 29
= 2552 cm
2
5. A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find the total
surface area of the solid thus generated.
Solution:
We have,
Dimension of rectangular strip = 25 cm × 7cm
When this strip is rotated about its longer side,
Height of cylinder becomes = 25 cm
Radius = 7 cm
? Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7 (25 + 7)
= 2 × 22/7 × 7 × 32
= 1408 cm
2
6. A rectangular sheet of paper, 44 cm× 20 cm, is rolled along its length to form a
cylinder. Find the total surface area of the cylinder thus generated.
Solution:
We have,
Dimensions of rectangular sheet of paper = 44cm × 20cm
When this sheet of paper is rolled along its length,
Circumference of base becomes = 44 cm
By using the formula,
Circumference of base = 2pr
So, 2pr = 44
2 × 22/7 × r = 44
r = 44×7 / 44
= 7cm
Radius = 7cm
Height = 20cm
? Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7 (20 + 7)
= 2 × 22/7 × 7 × 27
= 1188 cm
2
7. 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 curved surface areas.
Solution:
We have,
Ratio of radius of two cylinder, r
1
:r
2
= 2:3
Ratio of their heights, h
1
:h
2
= 5:3
r
1
/r
2
= 2/3
h
1
/h
2
= 5/3
so,
Curved surface area of cylinder1 / curved surface area of cylinder2 = 2pr
1
h
1
/ 2pr
2
h
2
= (2 × 22/7 × 2 × 5) / (2 × 22/7 × 3 × 3)
= 10/9
? Ratio of their curved surface area is 10:9
8. The ratio between the curved surface area and the total surface area of a right
circular cylinder is 1:2. Prove that its height and radius are equal.
Solution:
We have,
Let radius of cylinder be ‘r’
Let height of cylinder be ‘h’
Curved surface area of cylinder / total surface area of cylinder = 1/2
2prh / 2pr (h+r) = 1/2
h/(h+r) = 1/2
2h = h+r
2h – h = r
h = r
Height = Radius
Hence proved.
9. The curved surface area of a cylinder is 1320 cm
2
and its base has diameter 21
cm. Find the height of the cylinder.
Solution:
We have,
Diameter of base = 21 cm
Radius of cylinder = 21/2 cm
Let height of cylinder be ‘h’ cm
Curved surface area of cylinder = 1320 cm
2
By using the formula,
Curved surface area of cylinder = 2prh
So,
2prh = 1320
2 × 22/7 × 21/2 × h = 1320
66h = 1320
h = 1320/66 = 20cm
Page 5
1. Find the curved surface area and total surface area of a cylinder, the diameter of
whose base is 7 cm and height is 60 cm.
Solution:
We have,
Diameter of cylinder = 7 cm
So, Radius of cylinder = 7/2 cm
Height of cylinder = 60 cm
By using the formula,
Curved surface area of cylinder = 2prh
= 2 × 22/7 × 7/2 × 60
= 1320 cm
2
Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7/2 (60 + 7/2)
= 22 (127/2)
= 1397 cm
2
2. The curved surface area of a cylindrical road is 132 cm
2
. Find its length if the
radius is 0.35 cm.
Solution:
We have,
Curved surface area of cylindrical road =132 cm
2
Radius of road = 0.35 cm
Let length of road be ‘h’ cm
By using the formula,
Curved surface area of cylindrical road = 2prh
So, 2prh = 132
2 × 22/7 × 0.35 × h = 132
h = 132×7 / 2×22×0.35
= 924 / 15.4
= 60cm
? Length of road is 60 cm.
3. The area of the base of a right circular cylinder is 616 cm
2
and its height is 2.5 cm.
Find the curved surface area of the cylinder.
Solution:
We have,
Area of base of right circular cylinder = 616 cm
2
Height of cylinder = 2.5 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
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 2.5
= 1540/7
= 220 cm
2
4. The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find
its curved surface area and total surface area.
Solution:
We have,
Circumference of base of cylinder = 88 cm
Height of cylinder = 15 cm
By using the formula,
Circumference of base of cylinder = 2pr
So,
2pr = 88
2 × 22/7 × r = 88
r = 88×7 / 44
= 616/44
= 14cm
Radius of cylinder = 14 cm
? Curved surface area of cylinder = 2prh
= 2 × 22/7 × 14 × 15
= 1320 cm
2
? Total surface area area of cylinder = 2pr (h+r)
= 2 × 22/7 × 14 (15 + 14)
= 2 × 22/7 × 14 × 29
= 2552 cm
2
5. A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find the total
surface area of the solid thus generated.
Solution:
We have,
Dimension of rectangular strip = 25 cm × 7cm
When this strip is rotated about its longer side,
Height of cylinder becomes = 25 cm
Radius = 7 cm
? Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7 (25 + 7)
= 2 × 22/7 × 7 × 32
= 1408 cm
2
6. A rectangular sheet of paper, 44 cm× 20 cm, is rolled along its length to form a
cylinder. Find the total surface area of the cylinder thus generated.
Solution:
We have,
Dimensions of rectangular sheet of paper = 44cm × 20cm
When this sheet of paper is rolled along its length,
Circumference of base becomes = 44 cm
By using the formula,
Circumference of base = 2pr
So, 2pr = 44
2 × 22/7 × r = 44
r = 44×7 / 44
= 7cm
Radius = 7cm
Height = 20cm
? Total surface area of cylinder = 2pr (h+r)
= 2 × 22/7 × 7 (20 + 7)
= 2 × 22/7 × 7 × 27
= 1188 cm
2
7. 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 curved surface areas.
Solution:
We have,
Ratio of radius of two cylinder, r
1
:r
2
= 2:3
Ratio of their heights, h
1
:h
2
= 5:3
r
1
/r
2
= 2/3
h
1
/h
2
= 5/3
so,
Curved surface area of cylinder1 / curved surface area of cylinder2 = 2pr
1
h
1
/ 2pr
2
h
2
= (2 × 22/7 × 2 × 5) / (2 × 22/7 × 3 × 3)
= 10/9
? Ratio of their curved surface area is 10:9
8. The ratio between the curved surface area and the total surface area of a right
circular cylinder is 1:2. Prove that its height and radius are equal.
Solution:
We have,
Let radius of cylinder be ‘r’
Let height of cylinder be ‘h’
Curved surface area of cylinder / total surface area of cylinder = 1/2
2prh / 2pr (h+r) = 1/2
h/(h+r) = 1/2
2h = h+r
2h – h = r
h = r
Height = Radius
Hence proved.
9. The curved surface area of a cylinder is 1320 cm
2
and its base has diameter 21
cm. Find the height of the cylinder.
Solution:
We have,
Diameter of base = 21 cm
Radius of cylinder = 21/2 cm
Let height of cylinder be ‘h’ cm
Curved surface area of cylinder = 1320 cm
2
By using the formula,
Curved surface area of cylinder = 2prh
So,
2prh = 1320
2 × 22/7 × 21/2 × h = 1320
66h = 1320
h = 1320/66 = 20cm
? Height of cylinder is 20cm.
10. The height of a right circular cylinder is 10.5 cm. If three times the sum of the
areas of its two circular faces is twice the area of the curved surface area. Find the
radius of its base.
Solution:
We have,
Height of cylinder = 10.5 cm
Let radius of cylinder be ‘r’ cm
So,
Area of two bases of cylinder = 2pr
2
Area of curved surface of cylinder = 2prh
Now,
3 (2pr
2
) = 2 (2prh)
6pr
2
= 4prh
pr
2
/ pr = 4/6 h
r = 2/3 h
= 2×10.5 /3
= 7cm
? Radius of base of cylinder is 7cm.
11. Find the cost of plastering the inner surface of a well at Rs 9.50 per m
2
, if it is 21
m deep and diameter of its top is 6 m.
Solution:
We have,
Height of cylinder = 21m
Diameter of cylinder = 6m
Radius of cylinder = 6/2 = 3m
Curved surface area of cylinder = 2prh
= 2 × 22/7 × 3 × 21
= 396 m
2
? Cost of plastering the inner surface at the rate of Rs 9.50 per m
2
= 396 × 9.50 = Rs
3762
12. A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find
the cost of tin-plating it on the inside at the rate of 50 paise per hundred square
centimetre.
Solution:
We have,
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