AnswersFL-1205040-MJ Grade 7 Mathematics B -GFVolume and Surface Area Problems

Volume and Surface Area Problems — Unit test Answers

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1
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Ryan and Scott are each studying a square pyramid.Which statement best describes the two pyramids?

Question illustration
A
Both pyramids have the same total surface area, but the areas of the lateral faces and the areas of the bases are different in each pyramid.
B
Both pyramids have the same total surface area, and the areas of the lateral faces and the areas of the bases are the same in each pyramid.
C
Ryan’s pyramid has a greater surface area.
D
Scott’s pyramid has a greater surface area.
2
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Carlos needs to paint the outside of the shed in his backyard, including its roof but not including its floor.What is the total area of the surfaces that he needs to paint?

Question illustration
A
214 feet squared
Option A
B
230 feet squared
Option B
C
300 feet squared
Option C
D
350 feet squared
Option D
3

Which could be the area of one face of the rectangular prism? Select three options. [Not drawn to scale]

Question illustration
A
24 square inches
B
28 square inches
C
36 square inches
D
54 square inches
E
63 square inches
4

Two isosceles triangular prisms were joined at their bases to form the composite solid shown. The width of base of both prisms is 6 units. What is the surface area of this composite solid?___________ square units

Question illustration
A
104
B
122
C
158
D
208
5

Nikolas calculated the volume of the prism. His work is shown below.Nikolas’s Work:Where, if any, did Nikolas first make a mistake in his work?

Question illustration
A
Nikolas used the wrong measurements when finding the area of the base.
B
Nikolas used the wrong formula for the volume of the prism.
C
Nikolas made a computational error.
D
Nikolas did not make a mistake.
6

Alexia set up the tent below in case it rained during the barbecue. Which equation shows how to determine the volume of the tent?

Question illustration
A
V = 7 (8) (12) + one-third (2) (8) (12)
Option A
B
V = 7 (8) (12) + one-half (2) (8) (12)
Option B
C
V = 7 (8) (12) + one-third (2) (7) (12)
Option C
D
V = 7 (8) (12) + one-half (2) (7) (12)
Option D
7

Jeremy constructed this solid by combining two rectangular prisms and a square pyramid. What is the surface area of this figure? _____________ square meters

Question illustration
A
320
B
322
C
368
D
386
8

Won has a container with the shape below. Which statements are true about the container? Select three options.

Question illustration
A
The shape can be broken into a rectangular prism and a triangular prism.
B
The shape can be broken into a rectangular prism and a rectangular pyramid.
C
The formula for the volume of this figure is .
Option C
D
The volume of the container is .
Option D
E
The volume of the container is .
Option E
9

A wooden block in the shape of a rectangular prism is cut into two congruent pieces. Which statement best compares the surface areas of the pieces to the surface area of the original block?

A
The surface area of each piece is equal to the surface area of the original block.
Option A
B
The surface area of each piece is equal to the sum of half the surface area of the original block plus half the area of the face created by the cut.
C
The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.
D
The surface area of each piece is equal to the surface area of the original block minus the area of the face created by the cut.
10

Which correctly describes a cross section of the square pyramid? Select three options.

Question illustration
A
A cross section parallel to the base is a square with side lengths of 2 ft.
B
A cross section parallel to the base is a square with side lengths of less than 2 ft.
C
A cross section perpendicular to the base through the top vertex is a triangle with the same dimensions as the triangular sides of the pyramid.
D
A cross section perpendicular to the base through the top vertex is a triangle with different dimensions than the triangular sides of the pyramid.
E
A cross section that is perpendicular to the base that does not pass through the top vertex of the pyramid is a trapezoid.
11

Which could be the area of one face of the triangular prism? Select three options. [Not drawn to scale]

Question illustration
A
24 square units
B
48 square units
C
72 square units
D
96 square units
E
144 square units
12

A rectangular prism has a length of 8 feet, a width of 3 feet, and a height of 5 feet. What is the surface area of the rectangular prism?

A
64 square feet
B
79 square feet
C
120 square feet
D
158 square feet
13

The rectangular prism is to be sliced parallel to the shaded base. What number is missing from the dimensions of the cross section?_______ inches by 3 inches

Question illustration
A
3
B
4
C
6
D
7
14

Which statement is true about the square pyramid below?

Question illustration
A
The base has an area of 464 square inches.
B
The base has an area of 928 square inches.
C
Each of the lateral faces has an area of 464 square inches.
D
Each of the lateral faces has an area of 928 square inches.
15

A square prism was sliced not perpendicular to its base and not through any of its vertices. What is the shape of the cross section shown in the figure?

Question illustration
A
a parallelogram that is not a rectangle or square
B
a rectangle that is not a square
C
a square
D
a trapezoid

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