Math 10Chapter 1 - Geometry of 3-D Figures

Lesson 4 – Calculating Surface Areas of 3-D Shapes

Todays Objectives: In this section we will:

Sketch a diagram to represent a problem that involves surface area (SA)

Determine the SA of a right cone, right prism, right pyramid, or sphere using an object or diagram

Determine an unknown dimension of a right cone, right prism, right pyramid, or sphere given the SA and remaining dimensions

Solve a problem that involves SA

Surface Area Area is the two-dimensional (2-D) size of a

surface. Consider the area that your notebook is covering on the surface of your desk

Surface area (SA) of a solid is the total area of the exposed surfaces of a three-dimensional (3-D) object.

Surface Area Consider a box. If you unfolded the sides,

top, bottom, front and back…how much area on your desk would it cover?

That would be the surface area of the box

Review of areas

Surface Area Formulas

h = height

r = radius

s = slant height

Examples1. Height is 7 feet. Radius is 2 feet.

Label the cone and then solve the surface area.

Answer = 58 square feet

2. Lateral area is 220 square cms. Diameter is 10cm. What is the height of the cone?

Answer = 13.1 cm

Surface Area Formulas Right Pyramid

Atriangle = 1/2bs Abase = b2

SA = 2bs + b2

Right pyramid is a 3D object with triangular faces and a polygon base

Examples1. Slant height is 10 cm. Base length is 8cm.

Label the triangle and then solve the surface area.Answer = 224

square cm2. Slant height is 7.8 cm. Triangular base length is 9cm.

Label the triangle and then solve the surface area. Answer = 140.4

square cm

Surface Area Formulas

Right Prism SA = 2(hl + lw + hw)

Surface Area Formulas

Example

Answer = 1508 square cm

Height is 8 cm. Diameter is 24cm.

Draw and label the cylinder and then solve the surface area.

Surface Area Formulas

½ of sphere

Examples

Diameter is 16cm.

Draw and label the sphere and then solve the surface area.

Answer = 804 square cm

Combined Surface Areas Sometimes you may encounter 2 or more

shapes combined into one *Don’t forget that you may need to subtract and/or

add certain dimensions to find the correct answer Ex.) How can we find the SA of this shape?

Answer!

51254 sq. in