9 cm

12 cm

6 cm

6 cm

A&W Math 11 Ch. 3.1 Surface Area of Prisms (Part I) Notes

Review:

Example 1: Find the area of the shapes below (not drawn to scale)

12.2m

4.7m

5”

4.7”

PRISM:

RECTANGULAR PRISM:

TRIANGULAR PRISM:

NET:

Example 2: If this right pentagonal prism were made from one piece of cardboard, what

would the piece of cardboard look like?

Example 3: Nicholas ships posters and reproduction art prints to customers in shipping

boxes made in the shape of an equilateral triangular prism, as shown in the diagram.

a) Draw a net of the box and label the dimensions of each side.

b) Calculate the surface area of the box.

Homework: Pg. 131 #3-4 Pg. 138 #8ab Pg. 142 #9-10

Example 4: A hexomino is a shape made of six identical squares connected along their

sides. There are 35 different patterns that can be made from six squares to create 35

hexominos. Below are five different hexominos.

Which of these hexominos can be folded to form a closed cube?

Example 5: Find the surface area of the following shape

A&W Math 11 Ch. 3.1 Surface Area of Prisms (Part II) Notes

Example 1: Mignmei builds a shipping crate out of �

�" plywood. The crate is a cube with a

side dimension of 3 feet.

a) What is the surface area of the crate?

b) She buys plywood in standard sheet sizes of 4 ft x 8 ft. How many sheets of plywood

does she need to build one shipping crate?

c) She builds a second crate that is twice the height, but has the same length and width.

What is the surface area of the second crate? How many sheets of plywood will she

need to build the larger shipping crate? Explain.

Example 2: Dirk fabricates a section of furnace duct out of sheet metal. What is the total

area of sheet metal that he needs? The duct is open at the upper right face and the left

bottom face.

Homework: Pg. 145 #11-12 Pg. 146 #1-4

Example 3: Calculate the surface area of the shape below.

A&W Math 11 Ch. 3.2 Surface Area of Cylinders Notes

Review: Example 1: Find the area of the shapes below (not drawn to scale) Find the area of the shaded portion

3 cm

CYLINDER:

Example 2: Draw the net of the cylinder below and find the surface area. SURFACE AREA CYLINDER: Example 3: Find the surface area of a container that has a radius of 15 cm and a height of 21 cm.

Homework: Pg. 150 #1,3 Pg. 153 #4-6

Example 4: Find the surface area of the figure below. Example 5: What is the height of a cylinder with surface area of 339 in2 and a radius of 3”?

A&W Math 11 Ch. 3.2 Surface Area of Pyramids Notes

PYRAMID: Example 1: Draw the net of the pyramid below and find the surface area. What do you do when you aren’t given the slant height? Example 2: Find the surface area of the square-based pyramid below.

Homework: Pg. 155 #7-9 Pg. 158 #10,11

Example 3: Find the surface area of the tetrahedron (Triangular based Pyramid) below. (All 4 sides are the same size) LATERAL AREA: Shade the lateral area of the pyramids below

A&W Math 11 Ch. 3.2 Surface Area of Cones Notes

CONE: Example 1: Draw a cone with its corresponding Net. SURFACE AREA CONE: Example 2: Find the surface area of a cone that has a slant height of 25” and a diameter of 6”.

Homework: Pg. 161 #13-14 Pg. 162 #15-17

Example 3: Find the surface area of the cone. Example 4: Find the lateral surface area of a cone whose height is 27 cm and whose diameter is 12 cm Example 5: Find the height of a cone with surface area of 75.4 m2 and a radius of 3 m

A&W 11 Ch. 3.2 Surface Area of Spheres & Composite Shapes Notes

SPHERE: SURFACE AREA SPHERE: Example 1: Find the surface area of a sphere with a diameter of 3’

Example 2: Find the surface area of a hemisphere with a radius of 38 cm Example 3: What is the diameter of a sphere with a surface area of 1256 cm2

Example 4: Sunny has been contracted by a company to design a large balloon for the city’s parade. He makes a sketch of his design, as shown below. Find the surface area of the balloon

Homework: Pg. 164 #18-20 Pg. 166 #21-23

Example 5: Find the surface area of the composite shape below

Homework: Pg. 167 #1-6

A&W 11 Ch. 3.2 Surface Area Review Notes

Example 1: A grain silo is in the shape of a cylinder, and it has a dome-shaped roof. It has the following dimensions: r = 3.5 m h = 20m a) It is being repainted. What is the surface area that will need to be painted? b) A quart of paint usually covers 25 m2. How many quarts are needed? c) If a quart of paint costs $35.49 how much will be spent on the paint (before taxes)

A&W Math 11 Ch. 3.3 Volume & Capacity of Prisms and Cylinders

Volume:

Capacity:

Volume of ALL Prisms:

Example 1: Find the volume of the following objects

a) b)

c)

Example 2: Luis sells different sizes of fish tanks in his pet store.

a) How much water will be needed to completely fill each tank?

b) Look at tanks 2 and 3. How many dimensions have changed? By how much? How

does the volume of tank 2 compare with tank 3?

c) Look at tanks 1 and 3. How many dimensions have changed? By how much? How

does the volume of tank 1 compare with that of tank 3?

d) One litre equals 1000 cubic centimetres. Convert the volumes of the fish tanks to

capacity in litres.

Example 3: Engine displacement is the volume swept by the pistons in an engine’s

cylinders. The following formula can be used to calculate engine displacement.

��������������� = � �����2 ��(� ����)(#����������)

The bore is the diameter of the engine’s cylinder. The stroke is the distance that the piston

moves in the cylinder.

A 4-Cylinder engine has a bore of 75.5 mm and a stroke of 82 mm.

a) What is the engine displacement in cm3?

b) Engine displacement is commonly stated in litres. What is the displacement, in litres,

of this engine? (Hint: One litre equals 1000 cm3)

c) Until recently, the engine displacement of cars manufactured in the United States

was stated in cubic inches. What is the displacement, in cubic inche, of the engine in

part a)? (Hint: One inch equals 2.54 cm)

Example 4: A community swimming pool is 100 feet long and 50 feet wide. It is 7feet

deep at the deep end and has a beach entry (0 feet deep) at the shallow end. The bottom

of the pool has a constant slope.

a) Sketch the shape of the pool and label the dimensions.

b) What is the water capacity of the pool in cubic feet and in US gallons?

(one cubic foot = 7.48 US gallons.)

c) What is the surface area of the inside of the pool?

Example 5: Find the volume of the composite shape below

Example 6: A cylindrical can has a capacity of 4.2L. If the can has a diameter of 21 cm.

What is the height of the can? (Round your answer to the nearest tenth of a cm)

Assignment: Pg. 176 #6-7 Pg. 178 #9-10 Pg. 179 #1-6

A&W 11 Ch. 3.4 Volume & Capacity of Spheres, Cones & Pyramids

Volume of Sphere:

Volume of Cone:

Volume of Pyramid

Example 1: A tennis ball has a diameter of 6.7 cm.

a) What is the volume of the tennis ball?

b) Tennis balls are commonly sold in a cylindrical tube in packs of three balls per tube.

What is the volume of the container?

c) What is the ratio of the volume of the three balls to the volume of the container?

Example 2:Mikhail is casting garden gnomes out of concrete. He wants to know how much

concrete he will need to make 20 gnomes. Because the gnomes are an irregular shape, he

approximates the gnome as a series of simpler shapes: the hat is a cone, the head is a

hemisphere, and the body is a cylinder. What volume of concrete in cubic feet will he need

for 20 gnomes?

Example 3: Jayne built a model of a house using a rectangular prism for the base and a

rectangular pyramid for the roof. If the model is solid, what is the volume of her model?

Example 4: A cone has a slant height of 18 inches and diameter of 8 inches. Determine its

volume.

Example 5: A rectangular based pyramid with base measurements of 10 cm by 16 cm, and

its height is 37 cm. A cone has a diameter of 15 cm and also has a height of 45 cm.

a) What is the difference in volume between the two figures?

b) What is the difference in capacity?

Assignment: Pg. 184 #2 Pg. 186 #4 Pg. 191 #7-9 Pg. 193 #1-5