Grade 7 Math Practice Test: Surface Area of Prisms and Cross Sections
- Surface Area and Cross Sections
- 10 questions
- 15 minutes
This test covers the surface area of rectangular and triangular prisms, volume problems and the shapes you get when you slice a solid. Tip: surface area is the sum of the areas of all faces, so count each pair of matching faces.
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Question 1
What is the surface area of a rectangular prism that is 5 cm long, 3 cm wide and 2 cm high?
Correct answer: C
SA = 2(5·3 + 5·2 + 3·2) = 2(15 + 10 + 6) = 62 cm2. 30 is the volume in cm3, and 31 counts each face only once.
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Question 2
What is the surface area of a cube with 4 cm edges?
Correct answer: C
A cube has 6 square faces of 4 × 4 = 16 cm2, so 6 × 16 = 96 cm2. 64 is the volume in cm3.
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Question 3
A triangular prism has right-triangle bases with sides 3 cm, 4 cm and 5 cm. The prism is 10 cm long. What is its surface area?
Correct answer: C
Each base is 12 · 3 · 4 = 6 cm2, so both bases are 12 cm2. The three rectangles are (3 + 4 + 5) · 10 = 120 cm2. Total: 132 cm2. 126 counts only one base.
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Question 4
A cube is sliced by a plane parallel to one of its faces. What is the shape of the cross section?
Correct answer: D
A slice parallel to a face is a copy of that face, so it is a square the same size as each face. Triangles and hexagons appear only when the cut is tilted.
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Question 5
A right rectangular pyramid is sliced by a plane parallel to its base. What is the shape of the cross section?
Correct answer: B
A slice parallel to the base has the same shape as the base, only smaller, so it is a rectangle. A triangle appears when the cut is vertical through the top.
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Question 6
A right square pyramid is sliced by a vertical plane that passes through its top vertex and is perpendicular to the base. What is the shape of the cross section?
Correct answer: A
The cut goes from the base up to the single top point, so the cross section narrows to a point: a triangle. A square is the cross section of a cut parallel to the base.
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Question 7
A box is 2 ft by 3 ft by 4 ft. It rests on its 3 ft by 4 ft face. What area must be painted to cover every face except the bottom?
Correct answer: B
The full surface area is 2(6 + 8 + 12) = 52 ft2. Leaving out the 3 × 4 = 12 ft2 bottom gives 40 ft2. 46 leaves out a 2 × 3 face, which is not the bottom here.
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Question 8
A rectangular prism has a volume of 120 cm3, a length of 6 cm and a width of 4 cm. What is its height?
Correct answer: A
V = l · w · h, so 120 = 6 · 4 · h = 24h and h = 5 cm. 20 cm divides 120 by 6 only.
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Question 9
A triangular prism has a triangular base with base 6 cm and height 4 cm. The prism is 9 cm long. What is its volume?
Correct answer: D
The base area is 12 · 6 · 4 = 12 cm2, and 12 · 9 = 108 cm3. 216 forgets the 12 in the triangle area.
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Question 10
How many faces does a hexagonal prism have?
Correct answer: B
It has 2 hexagonal bases and 6 rectangular side faces: 8 faces. 12 is the number of its vertices.
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