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Yr12FM SAC 2 REVISION Geometry
Name: ___________________________
(SOLUTIONS)
Section A Multiple Choice
1
Examine the triangle in the following
figure.
4
The value of x is:
A 33
B 59
C 68
D 90
E 57
2
An appropriate name for the object is:
A rectangular prism
B rectangular pyramid
C triangular prism
D triangular pyramid
E trapezium prism
Examine the following figure.
5
The volume of a sphere with a diameter
of 15 cm is closest to:
A 560 π cm3
B 900 π cm3
C 4500 π cm3
D 36 000 π cm3
E 45 000 π cm3
6
The circumference of the base of the
larger cone is closest to:
The area of the shape is:
A (130 000 + 10 000π) mm²
B (160 000 + 10 000π) mm²
C (160 000 + 5000π) mm²
D (130 000 + 5000π) mm²
E 30 100 mm²
3
The total surface area of a closed
cylinder of radius 40 cm and height
20 cm is given by:
A 2  π  20  40
B 2  π  40  40
C 2  π  40  100
D 2  π  40  60
E 2  π  20  60
Consider the net of the following figure.
A
B
C
D
E
113 mm
151 mm
190 mm
302 mm
459 mm
1
7
If the height of a flag with
diagonal = 68 cm is 90 cm, then a
similar flag with diagonal = 34 cm has a
height closest to:
A 67 cm
B 45 cm
C 30 cm
D 26 cm
E 34 cm
8
The diagram shows the path of a light
beam hitting a mirror.
9
Find the length of the side a (to the
nearest m).
A 14 m
B 15 m
C 16 m
D 17 m
E 18 m
The expression for x is:
A
B
C
D
E
6 6 x

4
x
4 6 x

6
x
6 x6

4
x
12 6  x

6
x
6 2 x

4
x
A monster slice of pizza is made in the
shape below.
10
A large cone is filled to half its height
with water as shown.
The ratio of the volume of water to air
is:
A 1:7
B 1:8
C 8:1
D 1:9
E 1:2
2
11
Given that you have a two-litre and a
one-litre carton of milk in the same
shape (similar dimensions), the length
scale factor of the two-litre to the onelitre carton is:
A 2:1
B 1:2
C 2: 2
3
D
2:1
E 8:1
3
Yr12FM SAC 2 REVISION Geometry
Name: ___________________________
(SOLUTIONS)
Section B Short/Extended answer
1
For each of the figures, find the value of the
pronumeral.
(a)
5
(b)
2
Find the interior and exterior angles for each of
the following regular polygons.
(a) Octagon
(b) Heptagon
(c) Nonagon
3
4
3
Find the perimeter and area of the following
figures.
(a)
6
(b)
5
4
Examine the solid prism below.
3
(a) Sketch an appropriate net for the given
prism.
(b) Transfer the units appropriately to the net.
(c) Calculate the total surface area of the
object.
5
Examine the diagram below.
4
For the object shown:
(a) What is the volume contained by the solid
and framed sections (to 1 decimal place)?
(b) What is the volume of the solid part only?
6
6
The dimensions of a rectangular prism tub are
30 cm by 20 cm by 15 cm. The tub is filled
completely with water, and the water is
transferred into a cylindrical tank that is 10 cm
in radius and 40 cm tall. How high is the water
level in the cylinder?
5
7
Two ladders are placed against the wall at the
same angle. The ladders are 2 metres and
3 metres long. If the taller ladder reaches
2.1 metres up the wall, how far does the second
ladder reach (to 1 decimal place)?
3
8
Note the following measurements from the
buoy to the shore as shown in the diagram
below.
3
How far is it to the buoy (to the nearest metre)?
(This is the distance x on the diagram.)
7
9
A rectangular block of clay has dimensions
30 cm by 20 cm by 10 cm.
3
(a) What is the volume of the block of clay?
(b) Express in litres your answer from (a).
(c) What is the total surface area of the clay?
10
The clay from question 9 is remolded into a
cylinder with height 30 cm.
6
(a) Find the diameter of the cylindrical block
of clay (to 2 decimal places).
(b) Find the new total surface area of the clay
when molded as a cylinder (to the nearest
cm²).
(c) What fraction of the volume needs to be
removed to turn the cylindrical block into a
cone with the same diameter and height?
11
A windscreen wiper covers the shaded area
below.
3
Find the area of the rectangular windscreen that
is not covered by the windscreen wiper (to the
nearest cm²).
8