Learn on PengienVision, Mathematics, Grade 8Chapter 8: Solve Problems Involving Surface Area and Volume

Lesson 1: Find Surface Area of Three-Dimensional Figures

In this Grade 8 enVision Mathematics lesson from Chapter 8, students learn how to calculate the surface area of cylinders, cones, and spheres using the formulas S.A. = 2πr² + 2πrh, S.A. = πr² + πrℓ, and S.A. = 4πr². Students explore how nets and two-dimensional polygon areas connect to the lateral and base surfaces of three-dimensional figures.

Section 1

Finding Surface Area Using Nets

Property

A net is a 2D pattern that can be folded to form a 3D solid. To find surface area using nets:
(1) identify all faces in the net;
(2) calculate the area of each face;
(3) sum all areas: Surface Area = A1+A2+A3+...+AnA_1 + A_2 + A_3 + ... + A_n

Examples

Section 2

Lateral Surface Area of Cylinders

Property

The lateral surface area of a cylinder is the area of only the curved surface, excluding the circular bases: Slateral=2πrhS_{lateral} = 2\pi rh

Examples

Section 3

Step-by-Step Cylinder Surface Area Calculations

Property

To calculate cylinder surface area systematically:
(1) Identify radius rr and height hh,
(2) Calculate base areas: 2πr22\pi r^2,
(3) Calculate lateral area: 2πrh2\pi rh,
(4) Add components: S=2πr2+2πrhS = 2\pi r^2 + 2\pi rh

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Finding Surface Area Using Nets

Property

A net is a 2D pattern that can be folded to form a 3D solid. To find surface area using nets:
(1) identify all faces in the net;
(2) calculate the area of each face;
(3) sum all areas: Surface Area = A1+A2+A3+...+AnA_1 + A_2 + A_3 + ... + A_n

Examples

Section 2

Lateral Surface Area of Cylinders

Property

The lateral surface area of a cylinder is the area of only the curved surface, excluding the circular bases: Slateral=2πrhS_{lateral} = 2\pi rh

Examples

Section 3

Step-by-Step Cylinder Surface Area Calculations

Property

To calculate cylinder surface area systematically:
(1) Identify radius rr and height hh,
(2) Calculate base areas: 2πr22\pi r^2,
(3) Calculate lateral area: 2πrh2\pi rh,
(4) Add components: S=2πr2+2πrhS = 2\pi r^2 + 2\pi rh

Examples