Class 8 RD Sharma Solutions – Chapter 22 Mensuration III (Surface Area And Volume Of Right Circular Cylinder) – Exercise 22.1 | Set 1
Last Updated :
19 Sep, 2024
Chapter 22 of RD Sharma’s Class 8 Mathematics textbook, titled “Mensuration III,” focuses on the surface area and volume of right circular cylinders. Exercise 22.1 | Set 1 specifically deals with calculating the curved surface area, total surface area, and volume of cylinders.
This exercise introduces students to the fundamental formulas and concepts needed to solve problems related to cylindrical objects. Students learn to apply these formulas in various real-world scenarios, enhancing their spatial reasoning and problem-solving skills.
Question 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:
The details given about cylinder are:
Diameter of base of a cylinder = 7 cm
So, radius = (7/2)
Height of cylinder = 60 cm
Curved surface area of a cylinder = 2 * (22/7) * r * h
= 2 * (22/7) * (7/2) * 60
= 1320 cm2
Total surface area of cylinder = 2 * (22/7) * r * (h + r)
= 2 * (22/7) * (7/2) * (60 + (7/2))
= 22 * (60 * 2 + 7)/2
= 22 * (127/2)
= 1397 cm2
Question 2: The curved surface area of a cylindrical rod is 132 cm2. Find the length if the radius is 0.35 cm.
Solution:
The details given about cylindrical rod are –
Curved surface area of a cylindrical rod = 132 cm2
Length of radius = 0.35 cm
Let length of rod = h
Curved surface area of a cylinder = 2 * (22/7) * r * h
132 = 2 * (22/7) * 0.35 * h
(132 * 7)/(2 * 0.35 * 22) = h
h = 60 cm
Question 3: The area of the base of a right circular cylinder is 616 cm2 and its height is 2.5 cm. Find the curved surface area of cylinder.
Solution:
The details given about right circular cylinder are –
Area of the base of a right circular cylinder = 616 cm2
Height of right circular cylinder = 2.5 cm
Let radius of right circular cylinder = r
Area of base of a right circular cylinder = (22/7) * r2
616 = (22/7) * r2
(616 * 7)/22 = r2
196 = r2
r = 14 cm
Curved surface area of cylinder = 2 * (22/7) * r * h
= 2 * (22/7) * 14 * 2.5
= 220 cm2
Question 4: The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find its curved area and total surface area.
Solution:
The details given about cylinder are –
Circumference of the base of a cylinder = 88 cm
Height of a cylinder = 15 cm
Let radius of cylinder = r
Circumference of the base of a cylinder = 2 * (22/7) * r
88 = 2 * (22/7) * r
(88 * 7) = (2 * 22) * r
r = 14 cm
Curved surface area of cylinder = 2 * (22/7) * r * h
= 2 * (22/7) * 14 * 15
= 1320 cm2
Total surface area of cylinder = 2 * (22/7) * r * (h + r)
= 2 * (22/7) * 14 * (15 + 14)
= 2 * (22/7) * 14 * 19
= 2552 cm2
Question 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:
The details given about rectangular strip are –
Dimension of rectangular strip = 25 cm * 7 cm
When the strip is rotated about its longer side,
Height of the cylinder becomes = 25 cm
Radius of cylinder = 7 cm
Total surface area of cylinder = 2 * (22/7) * r * (h + r)
= 2 * (22/7) * 7 * (25 + 7)
= 2 * (22/7) * 7 * 32
= 1408 cm2
Question 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:
The details given about rectangular sheet of paper are –
Dimensions of rectangular sheet = 44 cm * 20 cm
When the sheet of the paper is rolled along its length,
Height of the cylinder = 20 cm
Circumference of base becomes = 44 cm
Let radius of base = r
Circumference of base = 2 * (22/7) * r
44 = 2 * (22/7) * r
(44 * 7)/(2 * 22) = r
r = 7 cm
Total surface area of cylinder = 2 * (22/7) * r * (h + r)
= 2 * (22/7) * 7 * (20 + 7)
= 2 * (22/7) * 7 * 27
= 1188 cm2
Question7: The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of curved surface areas.
Solution:
The details given cylinders are –
r1 / r2 = 2 : 3
h1 / h2 = 5 : 3
Curved surface area of cylinder 1/Curved surface area of cylinder 2 = (2 * (22/7) * r1 * h1 )/(2 * (22/7) * r2 * h2)
= (2 * (22/7) * 2 * 5)/(2 * (22/7) * 3 * 3)
= 10/9
Question 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:
Curved surface area of cylinder/Total surface area of a cylinder = 1/2
(2 * (22/7) * r * h)/(2 * (22/7) * r * (h + r) = 1/2
h/(h + r) = 1/2
2 * h = h + r
2h – h = r
h = r
Height = Radius
Hence, Proved.
Question 9: The curved surface area of cylinder is 1320 cm2 and its base has diameter 21 cm. Find the height of cylinder.
Solution:
The details given about cylinder are –
Curved surface area of cylinder = 1320 cm2
Diameter of base = 21 cm
So, radius = 21/2
Let height of cylinder = h
Curved surface area of cylinder = 2 * (22/7) * r * h
1320 = 2 * (22/7) * (21/2) * h
(1320 * 7 * 2)/(2 * 22 * 21) = h
h = 20 cm
Question 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:
The details given about cylinder are –
Height of circular cylinder = 10.5 cm
Let radius of cylinder = r
Area of two bases of cylinder = 2 * (22/7) * r2
Area of curved surface of cylinder = 2 * (22/7) * r * h
3 * (2 * (22/7) * r2) = 2 * (2 * (22/7) * r * h))
6 * r = 4 * h
6 * r = 4 * 10.5
r = (4 * 10.5)/6
r = 7 cm
Summary
Exercise 22.1 | Set 1 of Chapter 22 in RD Sharma’s Class 8 Mathematics textbook provides a comprehensive exploration of the surface area and volume of right circular cylinders. Through a variety of problems, students learn to apply the formulas for curved surface area (2Ï€rh), total surface area (2Ï€rh + 2Ï€r²), and volume (Ï€r²h) of cylinders. The exercise emphasizes the importance of unit conversion and precise calculations in solving real-world problems involving cylindrical objects. Students are challenged to work with different given parameters, such as radius, diameter, height, surface area, or volume, to find the missing measurements. This approach helps develop critical thinking and problem-solving skills, as students learn to analyze given information and determine the appropriate steps to solve each problem. By mastering these concepts, students gain a solid foundation in three-dimensional geometry, preparing them for more advanced topics in mathematics and practical applications in various fields of science and engineering.
FAQs on Surface Area And Volume Of Right Circular Cylinder
What is the difference between curved surface area and total surface area of a cylinder?
The curved surface area includes only the lateral surface of the cylinder (2πrh), while the total surface area includes both the lateral surface and the two circular bases (2πrh + 2πr²).
How do you find the height of a cylinder if you know its volume and radius?
Rearrange the volume formula V = πr²h to solve for h: h = V / (πr²).
Why is π (pi) used in cylinder formulas?
Ï€ is used because it represents the ratio of a circle’s circumference to its diameter, which is crucial in calculating the curved surface and circular bases of a cylinder.
How do you convert cubic centimeters to liters?
1 liter = 1000 cubic centimeters. To convert from cm³ to liters, divide by 1000.
Can these formulas be applied to any cylinder?
These formulas apply specifically to right circular cylinders, where the bases are perpendicular to the height. For oblique cylinders, different formulas are needed.