FMa 10
Mid term Review
Name:________________
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which referent best represents a length of 1 cm?
a. the height of a doorknob above the floor
b. the length of your forearm
c. the thickness of a dime
d. the width of your fingernail
____ 2. Which referent best represents a length of 1 yard?
a. the height of a doorknob above the floor
b. the length of your forearm
c. the width of your fingernail
d. the width of your hand
____ 3. A single piece of sheet music is 21.6 cm wide. A stack of 100 sheets is 1.2 cm tall. If a 5-in.
stack of sheet music was laid out with the sheets side-by-side, how long would it be, to the nearest
hundredth of a metre?
a. 35.24 m
c. 228.53 m
b. 51.42 m
d. 329.31 m
____ 4. A stack of 100 pieces of sheet music is 0.5 in. tall. How many pieces can fit in a storage
box that is 1 ft high?
a. 2 400 pieces
c. 400 pieces
b. 1 200 pieces
d. 200 pieces
The following question(s) are based on the 8-track cartridge shown below.
____ 5. What is the surface area of an 8-track cartridge that is 13.4 cm long,
10.0 cm wide, and 2.2 cm thick?
a. 58 cm2
b. 134 cm2
____
c. 186 cm2
d. 371 cm2
6. An 8-track cartridge is 5.3 in. long, 3.9 in. wide, and 0.9 in. high. The cartridge holds 45
min of music. A 12-in. vinyl LP record that is
in. thick holds the same amount of music as an 8-
track cartridge. Which device has the greater music capacity, in minutes per cubic inch, and by how
much?
c. the 8-track by 2.4 min./in3
a. the 8-track by 0.8 min./in3
3
b. the LP by 0.8 min./in
d. the LP by 3.2 min./in3
____ 7. An advertising model of an MP3 player has a height of 5.4 in., a width of 5.2 in., and a
depth of 1.3 in. Determine the volume of the model MP3 player, to the nearest tenth of a centimeter.
a. 30.2 cm3
b. 149.7 cm3
____
8. Determine the surface area of the right rectangular prism.
a. 177 cm2
b. 165 cm2
____
c. 598.2 cm3
d. 1047.3 cm3
c. 160 cm2
d. 150 cm2
9. What is the volume of a circular pool with a diameter of 10 m and a depth of 5 m?
a. 47 m3
b. 157 m3
c. 393 m3
d. 1571 m3
____ 10. A right rectangular prism has a length of 80 mm, a width of 52 mm, and a height of 115
mm. Determine the volume of the prism, to the nearest cubic centimetre.
a. 48 cm3
b. 478 cm3
c. 47 840 cm3
d. 478 400 cm3
____ 11. A right cone has a volume of 314.16 cm3 and a radius of 5 cm. What is the height, to the
nearest tenth of a centimetre?
a. 10.1 cm
b. 11.3 cm
____
c. 11.8 cm
d. 12.0 cm
12. A baseball is wrapped in leather. The diameter of the ball is
in. How much leather is
needed to cover the baseball, to the nearest hundredth of a square inch?
a. 12.54 in.2
b. 25.97 in.2
c. 31.33 in.2
d. 52.46 in.2
____ 13. A right cone has a radius of 10 cm and a height of 24 cm. Determine the slant height, to
the nearest centimetre.
a. 23cm
b. 24 cm
c. 25 cm
d. 26 cm
____ 14. The diameter of the base of a right cone is 12 cm. The height of the cone is 14 cm. What
is the lateral area of the cone, to the nearest square centimetre?
c. 287 cm2
d. 264 cm2
a. 452 cm2
b. 339 cm2
____ 15. A sphere has a radius of 12 cm. Determine the surface area, to the nearest square
centimetre.
a. 1921 cm2
b. 1820 cm2
____
16. Determine the length of x, to the nearest tenth of a metre.
a. 5.2 m
b. 9.3 m
____
c. 68.6 m
d. 75.7 m
18. Determine the length of x, to the nearest tenth of a centimetre.
a. 13.5 cm
b. 29.0 m
____
c. 12.3 m
d. 14.7 m
17. Determine the length of x, to the nearest tenth of a centimetre.
a. 13.5 cm
b. 29.0 m
____
c. 1810 cm2
d. 1746 cm2
c. 68.6 m
d. 75.7 m
19. Determine the length of x, to the nearest tenth of a metre.
a. 5.1 m
b. 11.7 m
c. 23.6 m
d. 24.1 m
____ 20. What is the value of tan 65° to 3 decimal places?
a. 0.423
c. 0.906
b. 0.700
d. 2.145
____
21. Determine the value of sin 38°, to 3 decimal places.
a. 0.380
b. 0.616
____
22. Calculate the value of cos 38° to 3 decimal places.
a. 0.380
b. 0.616
____
c. 51.4°
d. 62.0°
24. Determine the measure of A if sin A = 0.7813.
a. 38.0°
b. 38.6°
____
c. 0.781
d. 0.788
23. Determine the measure of A if tan A = 0.7813, to the nearest tenth of a degree.
a. 38.0°
b. 38.6°
____
c. 0.781
d. 0.788
c. 51.4°
d. 62.0°
25. Determine the measure of A if cos A = 0.7813.
a. 38.0°
b. 38.6°
c. 51.4°
d. 62.0°
____ 26. One hundred sheets of sheet music make a stack that is 1.2 cm high. How many sheets
can fit in a shelf that is 5 in. high?
a. 164 sheets
b. 236 sheets
c. 1058 sheets
d. 1524 sheets
____ 27. One section of a cabinet is 17 in. wide and 20 in. deep. What are the approximate
dimensions of the section, in SI units?
a. 51 cm wide and 43 cm deep
b. 43 cm wide and 51 cm deep
c. 7.9 cm wide and 6.7 cm deep
d. 6.7 cm wide and 7.9 cm deep
____ 28. A DVD case has a height of 19.0 cm, a width of 13.5 cm, and a depth of 1.4 cm. What is
the volume of the case, to the nearest centimetre?
a. 339 cm3
b. 359 cm3
c. 2560 cm3
d. 3591 cm3
Short Answer
1. Jessica has designed a storage cabinet to store her CDs and DVDs. The cabinet door can be
closed. The cabinet is a right rectangular prism that is 1 m wide, 60 cm deep and 2.4 m high.
Determine the volume of the cabinet to the nearest tenth of a cubic metre.
V = (width)(depth)(height)
V = (1)(0.60)(2.4)
V = 1.44
The volume of the cabinet is 1.4 m3.
2. The pyramid of Khufu is a right pyramid with a square base. One side of the base is 230 m; the
slant height is 186 m. Determine the surface area of the pyramid, including the base, to the nearest
square metre.
SA = B + lateral area
SA = (length)(width) + 4[ (length)(slant height)]
SA = (230)(230) + 4[ (230)(186)] SA = 52 900 + 4[ (42 780)]
SA = 52 900 + 85 560
SA = 138 460 m2
The surface area is 138 460 m2.
3. Jennifer has designed a stone sculpture composed of a square-based right
pyramid and a right rectangular prism. The pyramid’s base has sides 25 cm long
and the pyramid has a slant height of 18 cm. The rectangular prism is 30 cm
wide, 20 cm deep, and 40 cm high. Calculate the total exposed surface area of
the sculpture.
SApyramid = B + lateral area
SApyramid = (length)(width) + 4[ (length)(slant height)]
SApyramid = (25)(25) + 4[ (25)(18)] = 625 + 4[ (450)] = 625 + 900 = 1525
SArectangular prism = 2wd + 2dh + 2wh
SArectangular prism = 2(30)(20) + 2(20)(40) + 2(30)(40) = 1200 + 1600 + 2400 = 5200
SAcovered faces = 2(30)(20) = 1200
SAtotal = SApyramid + SArectangular prism – SAcovered faces = 1525 + 5200 – 1200 = 5525
The total exposed surface area of the sculpture is 5525 cm2.
4. The volume of a right rectangular prism is 56 cm3. Determine three possibilities for the
dimensions of the prism.
Possible responses include
• 1 cm x 2 cm x 28 cm
• 1 cm x 4 cm x 14 cm
• 1 cm x 7 cm x 8 cm
• 2 cm x 2 cm x 14 cm
• 2 cm x 4 cm x 7 cm
5. Christina received a gift in the mail. The gift was shipped in the gift box shown. Calculate the
largest volume that the gift box can hold, to the nearest cubic centimetre.
V = lwh
V = (36)(8)(16)
V = 4608
The largest volume the gift box can hold is 4608 cm3.
6. A sphere has a radius of 8 in. Determine the volume of the sphere to the nearest cubic inch.
The volume of the sphere is approximately 2145 in3.
7. A rubber hockey puck has a radius of 3.7 cm and a thickness of 2.6 cm. What is the volume of
rubber needed to make the puck, to the nearest cubic centimetre?
The volume of the puck is approximately 112 cm3.
8. A water storage tank has a right cylindrical base and a domed top. The base has a diameter of 10 m
and a height of 12 m. The top is half a sphere with the same diameter as the cylindrical base.
a) Determine the volume of the tank.
b) How many litres will the tank hold, to the nearest hundred litres?
a)
V = 942.478 + 261.799
V = 1204.277 m3
The volume of the tank is 1204.277 m3.
b) 1 m3 = 1000 L
1204.277(1000) = 1 204 277
The tank will hold approximately 1 204 300 L.
9. A conical paper cup for holding popcorn has a radius of 3 in. and a height of 6 in. How much
paper, to the nearest square inch, is used to make the cup?
s2 = r2 + h2 s2 = 32 + 62 s2 = 9 + 36 s2 = 45
SA = rs
SA = (3)(6.7) SA = 63.146...
Approximately 63 in.2 of paper is used to make the cup.
10. A conical pile of road salt has a radius of 10 ft and a height of 14 ft. What is the volume of road
salt in the pile, to the nearest cubic foot?
The volume of road salt in the pile is approximately 1466 ft3.
11. A right cone with a volume of 120 cm3 just fits inside a right cylindrical container. What is the
volume of the container?
A right cylinder has three times the volume of a right cone with the same
radius and height.
Volume of cylinder = 3(120) = 360
The volume of the cylinder is 360 cm3.
12. A baseball has a diameter of 7.4 cm. How much leather is needed to cover it, to the nearest
square centimetre?
Approximately 172 cm2 of leather is needed to cover the baseball.
13. A right cylindrical bird feeder needs painting. It has a diameter of 8 in. and a height of 12 in.
Three circles, each with a radius 1.5 in., have been cut from the lateral surface of the cylinder in
order for the birds to feed. Determine the area of the feeder that needs to be painted, to the nearest
tenth of a square inch.
SAcylinder = 2r2 + 2rh
Area of each cut-out circle = r2
SAtotal = surface area of cylinder – area of three circles
SAtotal = 2 r2 + 2 rh – 3( r2)
SAtotal = 2 (4)2 + 2 (4)(12) – 3( (1.5)2)
SAtotal = 100.531 + 301.593 – 21.206
SAtotal = 380.918...
The total surface area of the feeder that needs to be painted is approximately
380.9 sq in.
14. Explain how doubling the length of the sides of a square-based right pyramid affects the volume
of the pyramid.
V=
w2h
When the sides are doubled:
When the base sides are doubled, the volume of the pyramid is quadrupled.
15. To measure the width of a river, Kirstyn uses a large rock, an oak tree, and elm tree as reference
points. Determine the width of the river, to the nearest tenth of a metre.
The distance across the river is the distance between the
rock and the oak tree (RO).
The distance between the elm and oak trees (EO) is 12 m.
The tangent of REO is
The width of the river is approximately 36.9 m.
16. A field is 65 m long by 45 m wide. Petra walks diagonally across the field. What angle, with
respect to the width of the field, does Petra’s path make? Answer to the nearest degree.
The angle is approximately 55°
17. The side adjacent to the 74° angle in a right triangle is 6 cm long. How long is the hypotenuse,
to the nearest tenth of a centimetre?
The hypotenuse is approximately 21.8 cm.
18. The side opposite from the 50° angle in a right triangle is 6 cm long. Determine the length of the
hypotenuse.
The hypotenuse is approximately 7.8 cm.
19. Solve
. Express each measurement to the nearest whole unit.
Angle C is 60°.
Use the cosine ratio to determine the length of side AC.
Side AC is 23 units.
Use the tangent ratio to determine the length of BC.
Side BC is 12 units.
20. Solve
. Express each measurement to the nearest whole unit.
Angle C = 90° – 40° = 50°.
tan 40° =
BC =
AC
;
35
AC = 35 x tan 40° = 29.4 units
352  29.4 2  45.7 units
21. During take-off, a plane must rise at least 20 m during the first 1.5 km of flight to successfully
clear the runway.
What is the minimum angle the plane must make with the ground for a safe take-off, to the nearest
hundredth of a degree?
sin θ =
20
1500
;
θ = sin–1 (
20
) = 7.66°
1500
The minimum angle for a safe take off is 7.66°.
22. A wooden cabinet for china is 54 in. wide, 18 in. deep, and 58.5 in. high. The front is
completely glass. What is the surface area of the exterior part of the cabinet that is not glass?
Express your answer to the nearest square inch.
SAsides = 2(18)(58.5)
SAsides = 2106 in.2
SAtop and bottom = 2(18  54)
SAtop and bottom = 1944 in.2
SAback = (54)(58.5)
SAback = 3159 in.2
SAtotal = 2106 + 1944 + 3159
SAtotal = 7209 in.2
The surface area of the exterior part of the cabinet that is not glass is 7209 in.2