Calculating the Surface Area of a Cylinder

Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping Your questions Satisfaction meter 1

Calculating the What you will learn At the end of this lesson, you will be able to calculate the surface area of a cylinder by finding the area of the cylinder s faces calculate the surface area of a cylinder using a formula Agenda Cylinders in real life Review of concepts Properties of a cylinder Calculating area of a cylinder s faces Calculating surface area of a cylinder using a formula 2

Calculating the Real-Life Applications People in many professions calculate the surface area of cylinders. Engineers Manufacturers Designers tube production packaging painting Contractors pipe construction Agenda Cylinders in real life Review of concepts Properties of a cylinder Calculating surface area of a cylinder s faces Calculating surface area of a cylinder using a formula 3

Calculating the Definitions and Terms Area The number of square units required to cover a 2D object. Surface Area The number of square units required to cover the surface area of a 3D object. Definitions and Terms Circumference The distance around a circle. Diameter The distance across the centre of a circle. circumference diameter 4

Calculating the Definitions and Terms Face Polygons or 2D shapes of a 3D object. circular face of a cylinder Pi ( ) The ratio of the circumference of a circle to its diameter. Pi is approximately equal to 3.14. C 3.14 d Definitions and Terms Radius Half the diameter of a circle. Net The 2D pattern of 3D shape. 5

Calculating the History π What is Pi? Pi is the 16 th letter of the Greek alphabet. It represents the ratio of the circumference of a circle to its diameter. Pi is an infinite decimal. This means that it never ends or repeats. It is approximately equal to 3.14. Agenda Cylinders in real life Definitions and terms Properties of a cylinder Calculating surface area of a cylinder s faces Calculating surface area of a cylinder using a formula 6

Calculating the Definition A cylinder is a 3D shape with two congruent circles for faces. Labelling a Cylinder The circle faces of the cylinder are called the bases. The bases of the cylinder are congruent and parallel to each other. The perpendicular distance between the bases of the cylinder is the height. 7

Calculating the Question 1 The bases of a cylinder are: a) congruent b) parallel to each other c) circles d) all of the above Question 1 The bases of a cylinder are: a) congruent b) parallel to each other c) circles d) all of the above 8

Calculating the Question 2 A cylinder s height is which of the following measurements? a) width of the cylinder s base b) circumference of the cylinder c) perpendicular distance between the cylinder s bases Question 2 A cylinder s height is which of the following measurements? a) width of the cylinder s base b) circumference of the cylinder c) perpendicular distance between the cylinder s bases 9

Calculating the Agenda Cylinders in real life Definitions and terms Properties of a cylinder Calculating surface area of a cylinder s faces Calculating surface area of a cylinder using a formula Surface Area The surface area of a cylinder is the number of square units required to cover the entire surface of the cylinder. surface area 10

Calculating the The area of a cylinder can be calculated by reducing a cylinder to its net and finding the area of each shape in the net cylinder = net of cylinder A cylinder s net consists of two circles and one rectangle. one rectangle two circles 11

Calculating the The surface area of a cylinder is calculated by adding the area of the cylinder s two circles and one rectangle together. Area of Circle 1 + Area of Circle 2 + Area of Rectangle Surface Area of Cylinder Calculating Surface Area Example Calculate the surface area of Cylinder A. Cylinder A 12

Calculating the Calculating Surface Area Example Cylinder A = Net of Cylinder A Calculating Surface Area Example Cylinder A = Net of Cylinder A Height of cylinder = width of rectangle Circumference of cylinder = length of rectangle 13

Calculating the Example Area of Circle 1 Area = Pi x radius 2 A = πr 2 A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 Example Area of Circle 2 Area = Pi x radius 2 A = πr 2 A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 14

Calculating the Example Area of Rectangle Area = length x width A = l x w A = 31.4 x 20 A = 628 cm 2 length = circumference of Circle 1 or 2 Example Where the length of the rectangle is the circumference or perimeter of Circle A or B, and the width is the height of the cylinder. circumference of circle = length of rectangle circumference of circle = length of rectangle height of cylinder = width of rectangle 15

Calculating the Example Rectangle length calculation Circumference = Pi x diameter C = πd C = 3.14 x 10 C = 31.4 cm Rectangle length = 31.4 cm Example Surface Area of Cylinder A Area of Circle A 78.5 cm 2 + Area of Circle B 78.5 cm 2 + Area of Rectangle 628 cm 2 Surface Area 785 cm 2 16

Calculating the Question 3 What is the surface area of Cylinder B? a) 500 cm 2 b) 471 cm 2 c) 207 cm 2 Question 3 What is the surface area of Cylinder B? a) 500 cm 2 b) 471 cm 2 c) 207 cm 2 17

Calculating the Question 3 What is the surface area of Cylinder B? Circle 1 A = πr 2 A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 Circle 2 A = πr 2 A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 Rectangle A = l x w A = 31.4 x 10 A = 314 cm 2 Length = Circumference C = πd C = 3.14 x 10 C = 31.4 cm Surface Area Circle 1 + Circle 2 + Rectangle Surface Area Surface Area 78.5 + 78.5 + 314.0 471.0 cm 2 Calculating the surface area by adding the area of the shapes of the cylinder is time consuming. By adding the formulas together surface area can be found more easily. 18

Calculating the Agenda Cylinders in real life Definitions and terms Properties of a cylinder Calculating surface area of a cylinder s faces Calculating surface area of a cylinder using a formula Formula The formula to find the surface area of a cylinder is: Area = 2 x pi x radius 2 + 2 x pi x radius x height or A = 2πr 2 + 2πrh 19

Calculating the with a Formula Where: cylinder net length = circumference The formula for the area of 2 circles 2πr 2 + 2πrh The formula for the area of a rectangle with Formula Example Calculate the surface area of the Cylinder C using a formula. 20

Calculating the with Formula Example A = 2πr 2 + 2πrh A = 2 x 3.14 x 3 2 + 2 x 3.14 x 3 x 30 A = 6.28 x 9 + 6.28 x 3 x 30 A = 56.52 + 565.2 A = 621.72 m 2 The surface area of Cylinder C is 621.72 m 2. with Formula Example Manny needs to cover the surface area of a cylinder with paper for a science project. The cylinder is 20 cm tall and has a radius of 2 cm. How much paper will Manny need to cover the cylinder? 21

Calculating the with Formula Example A = 2πr 2 + 2πrh A = 2 x 3.14 x 2 2 + 2 x 3.14 x 2 x 20 A = 6.28 x 4 + 6.28 x 2 x 20 A = 25.12 + 251.2 A = 276.32 cm 2 Manny needs 276.32 cm 2 of paper to cover the cylinder. Question 4 What is the surface area of Cylinder D? a) 628 cm 2 b) 314 cm 2 c) 942 cm 2 22

Calculating the Question 4 What is the surface area of Cylinder D? a) 628 cm 2 b) 314 cm 2 c) 942 cm 2 A = 2πr 2 + 2πrh A = 2 x 3.14 x 10 2 + 2 x 3.14 x 10 x 5 A = 6.28 x 100 + 6.28 x 10 x 5 A = 628 + 314 A = 942 cm 2 The surface area of Cylinder D is 942 cm 2. Question 5 Maria, an engineer, is creating a part for an airplane that is the shape of a cylinder. The part is 2 metres high and has a diameter of 2 metres. Maria needs to coat the part in plastic and therefore needs to calculate the surface area of the cylinder. What is the surface area of the part? a) 18.84 m 2 b) 6.28 m 2 c) 50.24 m 2 23

Calculating the Question 5 Maria, an engineer, is creating a part for an airplane that is the shape of a cylinder. The part is 2 metres high and has a diameter of 2 metres. Maria needs to coat the part in plastic and therefore needs to calculate the surface area of the cylinder. What is the surface area of the part? a) 18.84 m 2 b) 6.28 m 2 c) 50.24 m 2 A = 2πr 2 + 2πrh : radius = ½ diameter A = 2 x 3.14 x 1 2 + 2 x 3.14 x 1 x 2 A = 6.28 x 1 + 6.28 x 1 x 2 A = 6.28 + 12.56 A = 18.84 m 2 The surface area of the part is 18.84 m. 2 Resources Algebra Lab www.algebralab.org/word/word.aspx?file= Geometry_SurfaceAreaVolumeCylinders.xml Math www.math.com/tables/geometry/surfareas.htm 24