MPM1D Exam Review
1.
Chapter 8 – Measurement Geometry
Find the measures of the unknown sides in the triangles below:
a)
b)
q
p
8 cm
25 cm
9 cm
15 cm
2. A rectangular lot measures 150 m by 200 m. Instead of walking along the outside of the lot, Alexei
hops a fence and walks along the diagonal of the lot. How much distance does he save?
3. Find the area of the following triangles.
a)
26 m
b)
6 cm
10 m
4 cm
4. Zach is planning to repaint the two gables on his house.
One of the gables is shown.
A can of paint covers 10 m2.
How many cans of paint does he need?
13 m
24 m
5. A school field has the dimensions shown.
a) Calculate the length of one lap of the track.
b) If Loreena ran 625 metres, how many laps did she run?
c) Calculate the area of the field.
6. An engine seal is circular in shape, with a square
cut-out to fit over a shaft, as shown to the right.
a) Calculate the area of rubber required to make the seal.
b) The inside and outside edges of the seal have a steel
wire embedded inside to add strength.
How much wire is needed?
2 cm
4 cm
7. Determine an expression for the shaded area of each figure.
a)
b)
c)
8. A DVD player came packaged in the box pictured to the right.
20 cm
a) Find the volume and surface area of the box.
DVD Player
b) Determine the box’s volume if all dimensions are doubled.
30 cm
40 cm
9. Matt made the ramp to the right to test his new Slinky.
Find the volume and surface area of the ramp.
10. A spherical storage tank has a diameter of 16m.
a) Find the surface area of the tank.
10
2
b) A can of paint costs $30 and covers 20m .
How much will it cost to paint the tank?
c) A new tank will be built with a surface area of 2000m2.
What radius will be required?
80 cm
cm
24 cm
11. Chris is organizing a track meet, and he’s rented the pyramid-shaped
changing tent on the right for the athletes. Find the tent’s volume,
as well as the amount of fabric used to make the tent.
12. A dozen tennis balls, each with a radius of 3.2 cm, are placed
in a box so that they just barely fit. The balls form a single
layer that measures 3 balls by 4 balls.
How much empty space is left in the box?
13. Sawdust from a woodworking lab is blown into a conical container
for recycling into other products. The container has a radius
of 1.5m and a height of 2m.
a) Find the area of aluminium needed to make the sides and top
of the container.
b) How much sawdust can the container hold?
2.5 m
1.4 m
1.4 m
14. A cone is truncated to make a paper cup as shown in the diagram to the right.
Calculate the amount of paper needed to make the cup,
as well as the amount of water this cup can hold.
15. A square-based pyramid has a volume of 100 m3
and a base area of 40 m2. What is its height?
cup
16. A pyramid and a prism, both with the same height,
each have a base area of 64 m2. How do their volumes compare?
17. A triangular piece of cheese has a volume of 146.4 cm3.
Find the thickness, t, of the cheese.
Chapter 8 Exam Review – Solutions
1a) 17cm b) 23.3cm 2) 100m 3a) 120m2 b) 12cm2 4) 6 5a) 170m b) 3.7 c) 1530.04m2 6a) 42.27cm2 b) 37.1cm
7a) A  R 2  r 2 b) A  4r 2  r 2 c) A  4r 2  r 2 8a) 24000cm3, 5200cm2 b) 192000cm3 9) 9600cm3,
5040cm2 10a) 804.25m2 b) $1230 c) 12.6m 11a) 1.50m3, 8.68m2 12) 1498.61cm3 13a) 18.85m2 b) 4.71m3
14a) 147.59cm2, 147.78cm3 15) 2.5m 16) volume of prism is 3 times larger 17) 3.2cm