Review: Surface Area (SA) of Right

Rectangular Prisms and Cylinders

A face of the prism

Surface Area of Right Rectangular Prisms

There are 6 faces

Surface Area of Right Rectangular Prisms

SA is the sum of the areas of its faces

Surface Area of Right Rectangular Prisms

SA = Area of top + Area of bottom + Area of front + Area of back + Area

of left + Area of right

Surface Area of Right Rectangular Prisms

Opposite faces are congruent (same):• Area of top and bottom are the same• Area of front and back are the same• Area of left and right are the same

So, SA = (2 x area of top face) + (2 x area of front face) + (2 x area of right

face)

Surface Area of Right Rectangular Prisms

What is the surface area of this right rectangular prism?

SA = (2 × 35 × 80) + (2 × 80 × 45) + (2 × 35 × 45) = 5600 + 7200 + 3150 = 15 950 cm²

Base 12 circular bases

Base 2

Curved surface is a rectangle

Curved Surface

Surface Area of a Cylinder

Area of Curved surface = 2πr x h

Area of a base = πr²

Area of 2 bases = 2πr²

Surface Area of a Cylinder

Area of Curved surface = 2πr x h

Area of a base = πr²

Area of 2 bases = 2πr²

SA of a cylinder =

(2πr x h) + 2πr²

Surface Area of a Cylinder

What is the surface area, SA, of this right cylinder?

SA = 2πr² + 2πrh =(2 × π × 2²) + (2 × π × 2 × 5) ≈ 87.9645 cm²

A face of the prism

Review: Volume (V) of Right Rectangular

Prisms and Cylinders

Volume is a space occupied by the prism

Volume (V) of Right Rectangular Prisms

= (Area of the bottom face) x (height)= A x h

Volume (V) of Right Rectangular Prisms

Determine the volume of this right rectangular prism

V = A × h = (4.0 × 6.0) x 1.5 = 24.0 × 1.5

= 36.0 m³

Volume = (Area of a base) x (height)= (πr²) x

h

Volume (V) of Right Cylinder

Determine the volume of this right cylinder

V = area of a base x height = πr² × h = π(5)² × 8

≈ 628.3 cm³

A Worksheet:Finish both sides by tomorrow

1.4 Surface Areas of Right Pyramids and Right Cones

Build Your Pyramids!

Right Pyramid• is a 3-dimensional (3-D) object that has triangular faces and a base that is

a polygon.

• is a 3-dimensional (3-D) object that has triangular faces and a base that is

a polygon.

WHAT IS A POLYGON?

• Polygons are 2-dimensional shapes. • They are made of straight lines, and the

shape is "closed" (all the lines connect ).

WHAT IS A POLYGON?

Polygon (straight sides)

Not a Polygon (has a curve)

Not a Polygon (open, not closed)

• The shape of the base determines the NAME of the

pyramid

Right Pyramid

• MUST know the vocabulary!• Apex = a point where triangular faces meet

• Slant height = a height of a triangular face

Right Pyramid

Regular Polygon =

Same sides and same angles

If a base is Regular Polygon, then the triangular faces are

congruent (same)

Surface Area of a Right Pyramid

The surface area of a right pyramid is the sum of the areas of the triangular faces and the

base

SA = Area of faces + Area of the base

Surface Area of a Right Pyramid

A review question!!!

WHAT IS THE AREA OF A TRIANGLE?

Surface Area of a Right Pyramid

The surface area of a right pyramid is the sum of the areas of the triangular faces and the

base

SA = Area of faces + Area of the base

• The surface area of a right pyramid is the sum of the areas of the triangular faces and the base

• SA = Area of faces x Area of the base

• REVIEW!!!• WHAT IS THE AREA OF A TRIANGLE?

Surface Area of a Right Pyramid

This right square pyramid has a slant height of 10 cm and a base side length of 8 cm. What is its

surface area?

Surface Area of a Right Pyramid

SA = Area of faces + Area of the base

Answer:The area, A, of each triangular face is:A = (8)· (10)A = 80The area, B, of the base is:B = (8)· (8)B = 64So, the surface area, SA, of the pyramid is:SA = 4A + BSA = 4· (80) + 64SA = 384The surface area of the pyramid is 384cm².

Surface Area of a Right Pyramid

Jeanne-Marie measured then recorded the lengths of the edges and slant height of this regular tetrahedron.

What is its surface area to the nearest square centimetre?

Answer: The regular tetrahedron has 4 congruent faces. Each face is

a triangle with base 9.0 cm and height 7.8 cm.

The area, A, of each face is:A = ½(9.0 cm)x (7.8 cm)

The surface area, SA, is:SA = 4 x ½ (9.0 cm)x(7.8 cm)SA = 140.4 cm²

The surface area of the tetrahedron is approximately 140 cm².

Surface Area of a Right Pyramid

POWERPOINT PRACTICE PROBLEMCalculate the surface area of this regular tetrahedron to the nearest square metre.

(Answer: 43 m2)

A right rectangular pyramid has base dimensions 8 ft. by 10 ft.,

and a height of 16 ft. Calculate the surface area of the pyramid to the

nearest square foot.• There are 4 triangular faces and a rectangular

base. (What do you need to know to calculate the AREAS

of each face?)• Sketch the pyramid and label its vertices.• Draw the slant heights on two adjacent

triangles.• Opposite triangular faces are congruent. • In ∆EFH, FH is ½ the length of BC, so FH is 4 ft.• EF is the height of the pyramid, which is 16 ft.

SA = Area of faces + Area of the base

To calculate AREA OF TRIANGULAR FACES (½ base x height) you need to

know their SLANT HEIGHTS!How can you calculate the slant height of each of the triangular faces?

To calculate AREA OF TRIANGULAR FACES (½ base x height) you need to

know their SLANT HEIGHTS!

Use the Pythagorean Theorem in right ∆EFH.

SA = Area of faces + Area of the base

How can you calculate the slant height of ∆EFH?

To calculate AREA OF TRIANGULAR FACES (½ base x height) you need to

know their SLANT HEIGHTS!

AREA of ∆EDC = ½ base x height (slant)

SA = Area of faces + Area of the base

Also, AREA of ∆EAB = 5√272

How can you calculate the slant height of ∆EFH?

To calculate AREA OF TRIANGULAR FACES (½ base x height) you need to

know their SLANT HEIGHTS!

Use the Pythagorean Theorem in right ∆EFG.

SA = Area of faces + Area of the base

How can you calculate the slant height of ∆EFG?

To calculate AREA OF TRIANGULAR FACES (½ base x height) you need to

know their SLANT HEIGHTS!

AREA of ∆EBC = ½ base x height (slant)

SA = Area of faces + Area of the base

Also, AREA of ∆EAD = 4√281

To calculate AREA OF TRIANGULAR FACES (½ base x height) you need to

know their SLANT HEIGHTS!AREA of the base □ DCBA = DC x CB

SA = Area of faces + Area of the base

SA = 5(√272) + 5(√272) + 54(√281) + 4(√281) + 80

= 379.0286 ≈ 379 ft2

POWERPOINT PRACTICE PROBLEMA right rectangular pyramid has base

dimensions 4 m by 6 m, and a height of 8 m. Calculate the surface area of the pyramid to

the nearest square metre.

Surface Area of any Right Pyramid with a Regular Polygon Base

Surface Area of any Right Pyramid with a Regular Polygon

Base

Each triangular face has base l and height s.

Area of each face: A = ½ (base)(height)A = ½(l)(s)

Area of 4 faces is:= 4 [½ (l)(s)] = 4(½ s)(l)

Area of 4 faces has a special name:

Lateral Area or AL

AL = 4(½ s)(l) = (½ s)(4l) • (4 l) is a perimeter of the base So, SA of any pyramid with a polygon base:

SA = Lateral Area + Area of base = AL + Area of base

= (½ s)(perimeter of base) + Area of base

Surface Area of any Right Pyramid with a Regular Polygon Base

Right Circular Cone• is a 3-dimensional (3-D) object that

has a circular base and a curved surface.

• MUST know the vocabulary!• Height = the perpendicular distance

from the apex to the base

• Slant height = the shortest distance on the curved surface between the apex and a point on the circumference of the base

A right cone has a base radius of 2 ft. and a height of 7 ft. Calculate the surface area of this cone to the

nearest square foot.

A right cone has a base radius of 2 ft. and a height of 7 ft. Calculate the surface area of this cone to the

nearest square foot.

POWERPOINT PRACTICE PROBLEMA right cone has a base radius of 4 m and a

height of 10 m. Calculate the surface area of this cone to the nearest square metre.

HOMEWORK

PAGE: 34 - 35

PROBLEMS: 4, 6, 8, 9, 10, 11, 18