MATHEMATICS 8
CHAPTER 7 – VOLUME
UNDERSTANDING VOLUME (7.1)
Date _____________
REVIEW
The base (of a prism or cylinder) is…
The base of a rectangular prism is ____________ ____________.
The base of a triangular prism is a ________________________ ____________.
The base of a cylinder is a ___________________ ____________.
The height (or a prism or cylinder) is...
The prisms and cylinders in this chapter are right prisms and right cylinders. The height of a right prism or
cylinder is perpendicular (at 90°) to its base.
Volume is...
As compared to…
Area is…
Example 1: Name each of the following shapes. Draw an arrow to the side that could be the base. Indicate
the height.
To determine the volume of a prism or a cylinder, we can use the formula:
Volume = Area of Base x Height
Example 2: Determine the volume of each right prism or cylinder.
Example 3: Calculate the volume for the following shapes.
Example 4:
a) If you construct a rectangular
prism with a base of 3 cm x 4
cm, what is the volume if the
height is 2 cm?
b) If you construct a rectangular
prism with a base of 2 cm x 3
cm, what is the volume if the
height is 4 cm?
c) What is the difference
between a 2 cm x 3 cm x 4 cm
rectangular prism and a 3 cm x
4 cm x 2 cm rectangular
prism?
Example 5: Nina has a rectangular fish tank that has a base of 600 cm2 and the depth of the water is 16
cm. She adds a decorative castle and finds that the water rises 0.6 cm.
a) What is the volume of water before she added
the castle?
c) What is the volume of the castle?
b) What is the volume (water + castle) after she
added the castle?
MATHEMATICS 8
CHAPTER 7 – VOLUME
VOLUME OF A PRISM (7.2)
Date _____________
To determine the volume of a prism or a cylinder, we can use the formula:
Volume = Area of Base x Height
Recall the following formulas:
Area of a rectangle:
A = l ×w
Area of a triangle:
A = b × h ÷ 2 or A =
Example 1: Determine the volume of the following rectangular prism.
Example 2: Determine the volume of the following cube.
Example 3: Show the different ways can you cut a rectangular prism into half.
How does the volume of the triangular prisms compare to the rectangular prisms?
1
×b ×h
2
Example 4: Determine the volume of the following triangular prism.
Example 5: Determine the volume of the following triangular prism.
Example 6: Frosted O’s cereal comes in boxes that measure 20 cm wide, 30 cm tall and 5 cm thick. If they
only come seven-eighths full, what volume of cereal does it contain?
MATHEMATICS 8
CHAPTER 7 – VOLUME
VOLUME OF A CYLINDER (7.3)
Date _____________
To determine the volume of a prism or a cylinder, we can use the formula:
Volume = Area of base x height
Recall the following formula:
Area of a circle:
A = π ×r2
where
π ≈ 3.14
and r = radius (and d = diameter = 2 × r )
Example 1: Estimate the volume for the following cylinders. Then, calculate the volume. Express your
answer to the nearest tenth of a cubic unit.
a)
ESTIMATE
CALCULATE
b)
ESTIMATE
CALCULATE
Example 2: Jessie buys a can of motor oil at Auto World. It is 15 cm tall and has a diameter of 12 cm.
How much motor oil is contained in the can?
Volume of liquids can
also be expressed in
millilitres. (1 cm3 = 1 mL)
Example 3: Brent buys whipped topping in a cylindrical spray can to make his dessert for dinner. It has a
5
full. How much whipped topping is in the can?
radius of 3 cm and is 18 cm tall. However, the can is only
8
Express your answer to the nearest cubic centimetre.
Example 4: Johnny wants to put 300 cm3 of water in a cylindrical water bottle. The base of the water
bottle has a diameter of 8 cm. How tall is the bottle if it is completely full? Express your answer to the
nearest centimetre.
MATHEMATICS 8
CHAPTER 7 – VOLUME
SOLVING PROBLEMS INVOLVING PRISMS AND
CYLINDERS (7.4)
Date _____________
Example 1: Toblerone chocolate bars are sold in packages that are triangular prisms. Each bar measures 5.6
cm along its base, is 5 cm high and 20 cm long. In her candy shop, Heather is going to stack the bars to make
a triangular prism display, but it must fit on a countertop that is only 50 cm wide.
a) How many Toblerone bars will be needed for the display?
b) What is the volume of the display?
Example 2: A section of pipe has an inner diameter of 12 cm and an outer diameter of 15 cm. What volume
of concrete was poured to produce a pipe that measures 5 m long? Express your answer to the nearest cubic
centimetre.
1 m = 100 cm
Example 3: Lance’s truck has a bed that measures 2.5 m x 1.2 m x 2 m. He has 105 m3 of garbage he needs
to haul to the dump. If each trip costs him $25, how much will it cost him to haul away all of his garbage
(assuming the top of each load is level with the top of the truck bed)?
Example 4: Pandora is sending her cousin a cylindrical container of cookies that she had baked. The
container has a diameter of 25 cm and a height of 12 cm. She plans on putting the container inside a
rectangular box that measures 28 cm on each side and is 15 cm high, and then filling the rest of the box with
foam peanuts. What volume of foam peanuts will she need?
Example 5: City workers must replace a cylindrical pipe with a radius of 0.9 m and a length of 20 m by a new
pipe of equal volume. However, the new pipe has a smaller radius of 0.7 m. How long must the new pipe be?
Express your answer to the nearest tenth of a metre.