Surface Area of 3D Shapes - Geometry and Measures

Introduction

• This worksheet teaches how to calculate the surface area of various 3D shapes.
• Each section includes a worked example, a guided question, and practice questions.

Section A: Surface Area of Cubes

Worked Example

1. Find the area of one face:
   • Example: 7 cm x 7 cm = 49 cm²
2. Calculate total surface area by multiplying the area of one face by 6:
   • 49 cm² x 6 = Total surface area

Guided Practice

• Repeat steps to find the surface area of given cubes.
• Practice calculating dimensions given total surface area.

Section B: Surface Area of Cuboids

Worked Example

1. Calculate area of three different faces (opposite faces are identical):
   • Example computations: 12 x 5 = 60 cm², 6 x 5 = 30 cm², 12 x 6 = 72 cm²
2. Sum areas and double to find total surface area:
   • (60 + 30 + 72) x 2 = Total surface area

Guided Practice

• Follow similar steps for given cuboid problems.

Section C: Surface Area of Cylinders

Worked Example

1. Calculate area of circular faces using circle area formula (πr²):
   • Example: double the area of one circle.
2. Calculate area of curved face:
   • Formula: Circumference x Height
3. Sum all areas to find total surface area.

Guided Practice

• Apply steps to find surface area and solve practice questions.

Section D: Surface Area of Pyramids

Worked Example

1. Find area of base:
   • For square base: length x width
2. Calculate area of triangular faces:
   • Multiply area of one triangular face by number of faces.
3. Sum base and triangular areas for total.

Guided Practice

• Use given dimensions for pyramid surface area calculations.

Section E: Surface Area of Cones

Worked Example

1. Calculate area of circular base:
   • Use formula πr²
2. Find area of curved surface:
   • Formula: π x radius x slant height
3. Sum areas to get total surface area.

Guided Practice

• Solve practice problems using similar methods.

Section F: Surface Area of Spheres

Worked Example

• Formula for surface area of sphere: 4πr²

Guided Practice

• Calculate given sphere problems using formula.

Section G: Surface Area of Composite Shapes

Worked Example

1. Identify outward-facing sides
   • Only count visible parts of each component shape.
2. Calculate surface areas of outward sides and sum up.

Guided Practice

• Apply method to composite shape challenges.

Additional Practice

• Each section provides practice questions to solidify understanding.
• Encouraged to refer back to worked examples if needed.

---

This worksheet serves as a comprehensive guide to understanding and calculating the surface area of various 3D shapes, including cubes, cuboids, cylinders, pyramids, cones, spheres, and composite shapes. Practice problems help reinforce the concepts presented.