Surface Area & Volume Test
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May 08, 2015
1.
Which parallelogram has an area of 24 m 2 and a
perimeter of 28 m?
2.
Name:
Answers
Look at the parallelogram below.
a
Dylan wants to split the parallelogram into two
congruent triangles.
b
c
Which expression can he use to find the area, in
square centimetres, of each triangle?
a
(25 x 5) ÷ 2
b
(25 x 5) x 2
c
(25 x 13) ÷ 2
d
(25 x 13) x 2
Strategy:
d
Think about the relationship between a
triangle and a parallelogram – a
triangle is half of a parallelogram.
Area of a Parallelogram
A = bxh
= 25 x 5
Strategy:
Think about how to find area of a
parallelogram.
Area of a Triangle
A = (b x h) ÷ 2
= (25 x 5) ÷ 2
Think about how to find perimeter of a
polygon.
Calculate perimeter and area for each
of the shapes.
I could see that the only possible
option was A.
/2
3.
Look at the two parallelograms below.
4.
Jakob paints the outside of the rectangular
prism below, except for the bottom.
What is the total area that he paints?
What is the minimum number of small
parallelograms needed to cover the larger
parallelogram completely?
a
16
b
63
c
126
d
252
a
108 cm2
b
123 cm2
c
132 cm2
d
150 cm2
Chantel’s Strategy:
Mason’s Strategy:
Calculate the area for each of the
shapes that make up this rectangular
prism.
Calculate the area for the small
parallelogram.
Then add all of the answers for area of
these shapes.
Calculate the area for the large
parallelogram.
Don’t forget it doesn’t have a bottom
so don’t add that in when you’re
adding the area of the faces up.
Multiply your answer for the small
parallelogram until you get the area of
the large parallelogram.
When I did all of that, I got option b.
That left me with option b.
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5.
Which shape below has an area of 12cm2?
6.
Consider the triangular prism pictured below.
a
b
The area of the triangular base is 36 cm2. The volume
of the triangular prism is 396 cm3.
What is the height of the triangular prism?
c
d
a
6 cm
b
9 cm
c
11 cm
d
12 cm
Josh’s Strategy:
Remember the formula for volume of a
triangular prism.
Charlotte Hay’s Strategy:
Remember the formula for area of a
parallelogram as well as a rectangle.
Calculate area for each of the shapes.
You will see that option d is the right
one.
Figure out which numbers that would
create the area of the triangular base of
36cm2 and one of the multiples was
6 x6 but that didn’t make any sense
because it is a triangular prism.
There’s another set of multiples that
that would work and that is 9 x 4
Since it told you to find the height, first
I tried;
4 x 9 x 15
4x9x8
Finally I tried 4 x 9 x 11 and that gave
me the correct height.
So it was option c.
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7.
The three-dimensional figure below was built
using cubes.
The area of one face of a cube is 4 cm2.
8.
What is the surface area of the cube?
What is the top view of this figure?
a
10 cm2
b
12 cm2
c
20 cm2
d
24 cm2
a
Charlotte Barnett’s Strategy:
b
Multiply the area of one of the faces of
the cube which is 4cm2 by 6 because
there are 6 faces.
c
This will give me 24cm2.
That means option d is the correct one.
d
Aidan’s Strategy:
I made a model of this with linking
cubes.
Then I looked down on it from above
and I saw that it was 4 cubes – which is
option c.
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9.
/5
Determine the surface area of the following polyhedrons: (15 marks)
a)
Rectangle #1
A
=lxw
= 12cm x 7 cm
= 84cm2
(2 x 84cm2 = 168 cm2)
Rectangle #2
A
=lxw
= 7cm x 5 cm
= 35cm2
(2 x 35cm2 = 70cm2)
Rectangle #3
A
=lxw
= 12cm x 5 cm
= 60cm2
(2 x 50cm2 = 120cm2)
168cm2
70cm2
+120cm2
358cm2
Therefore the surface area of the rectangular prism is 358cm2.
--------------------------------------------------------------------------------------------------------------------------/5
b)
60cm2
48cm2
36cm2
+108cm2
252cm2
Rectangle #1
A
=lxw
= 15cm x 4 cm
= 60cm2
Rectangle #2
A
=lxw
= 12cm x 4cm
= 48cm2
Rectangle #3
A
=lxw
= 9cm x 4cm
= 36cm2
Triangle
A
=bxh2
= 9cm x 12cm  2
= 108cm  2
= 54cm2
(2 x 54cm2 = 108cm2)
Therefore the surface area of the triangular prism is 252cm2.
--------------------------------------------------------------------------------------------------------------------------/5
c)
Rectangle #1
A
=lxw
= 14cm x 3cm
= 42cm2
(3 x 42cm2 = 126cm2)
Triangle
A
=bxh2
= 14cm x 12cm  2
= 168cm  2
= 84cm2
(2 x 84cm2 = 168cm2)
126cm2
+168cm2
294cm2
Therefore the surface area of the triangular prism is 294cm2.
10.
a)
Determine the volume of the following prisms: (9 marks)
V
=lxwxh
= 12cm x 5cm x 7cm
= 420cm3
V
=lxwxh2
= 9cm x 4cm x 12cm  2
= 432  2
= 216cm3
V
=lxwxh2
= 14cm x 3cm x 12cm  2
= 504  2
= 252cm3
/3
b)
/3
c)
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