Area Detectives
Surface Area
Volume & Powers
Net Attack
What Went Wrong?
100
A square has a side length of 6 centimeters.
What is its area?
A. 12 cm²
B. 24 cm²
C. 36 cm²
D. 36 cm3
C. 36 cm²
100
A rectangular prism has how many faces?
A. 4
B. 5
C. 6
D. 8
C. 6
100
What does 53 mean?
A. 5 + 3
B. 5 × 3
C. 5 × 5 × 5
D. 3 × 3 × 3 × 3 × 3
C. 5 × 5 × 5
100
What is a net of a three-dimensional shape?
A. A picture of the inside of the shape
B. A flat arrangement of the faces that can be folded into a polyhedron
C. A measurement of the shape's volume
D. A drawing of only the largest face
B. A flat arrangement of the faces that can be folded into a polyhedron
100
On their test, a student says 72 = 14
What mistake did the student make?
They added 7 instead of multiplying. Exponents tell us how many times to multiply the base by itself.
200
A rectangle is 4 inches long and 7 inches wide.
Which calculation finds its area?
A. 4 + 7
B. 4 × 7
C. 2(4 + 7)
D. 7 − 4
B. 4 × 7
200
Which statement best describes surface area?
A. The amount of space inside a solid
B. The total area of all the outside faces of a solid
C. The distance around a solid
D. The number of faces a solid has
B. The total area of all the outside faces of a solid
200
A cube has an edge length of 4 inches.
What is its volume?
A. 12 in³
B. 16 in³
C. 32 in³
D. 64 in³
D. 64 in³
200
A net has 2 triangles and 3 rectangles.
What three-dimensional shape (polyhedron) can this net make?
A. Cube
B. Square pyramid
C. Triangular prism
D. Rectangular prism
C. Triangular prism
200
On their test, a student says:
"The volume of a cube with edge length of 2 inches is 4 cubic inches"
What mistake did the student make?
The student did "length x width" (area of square)
Instead of "length x width x height" (2x2x2 = 23 = 8).
Found area of a square instead of volume of a cube.
300
A student says:
"A square has a side length of 8 cm, so its area is 16 cm² because 8 + 8 = 16."
Is the student correct?
A. Yes, because area means adding the sides.
B. Yes, because a square has four equal sides.
C. No, because the area is 8 × 8 = 64 cm².
D. No, because the area is 8 × 4 = 32 cm².
C. No, because the area is 8 × 8 = 64 cm².
300
A rectangular prism measures 4 cm × 3 cm × 2 cm.
What is its surface area?
A. 26 cm²
B. 36 cm²
C. 52 cm²
D. 72 cm²
C. 52 cm²
300
A cube has an edge length of 6 cm.
Select ALL expressions that represent its volume.
A. 6 + 6 + 6
B. 63
C. 6 × 6 × 6
D. 18
E. 216
B, C, and E
300
A student sees a net with 2 triangles and 3 rectangles and says:
"It must make a rectangular prism because it has rectangles."
What is the student's mistake?
A. A rectangular prism cannot have rectangles.
B. The student ignored the two triangular faces.
C. A triangular prism cannot have rectangles.
D. Nets never show the faces of a solid.
B. The student ignored the two triangular faces.
300
A student looks at this net and says:
"There are 5 faces, so the surface area is 5 square centimeters."
What's wrong with that reasoning?
Surface area is the total area of all the faces on a polyhedron NOT the total number of faces.
- There are 6 faces to find the area of.
- Each face is a square with an area of 64cm2
- S.Area = 64 x 6 = 384 cm2
400
A square has an area of 49 square centimeters.
What is the side length?
A. 6 cm
B. 7 cm
C. 14 cm
D. 24.5 cm
B. 7 cm
400
Two rectangular prisms have the same volume.
Must they have the same surface area?
A. Yes, always.
B. No, they can have different surface areas.
C. Yes, because volume and surface area are the same thing.
D. Only if they are cubes.
B. No, they can have different surface areas.
400
A student says:
"A cube with edge length 5 has a volume of 25 cubic units because 5 × 5 = 25."
What did the student actually find?
A. The cube's surface area
B. The area of one square face
C. The cube's perimeter
D. The cube's total volume
B. The area of one square face
400
What is the name of the polyhedron this net will make?
Triangular Prism
400
Harmony wants to know how much water would fill her backyard pool.
She begins by calculating the surface area of her pool.
What mistake did Harmony make?
Finding the water to fill the pool = volume, not surface area!
500
Which statement is always true about the area of a square?
A. It is found by adding all four side lengths.
B. It is found by multiplying the side length by 2.
C. It is found by multiplying the side length by itself.
D. It is always twice the perimeter.
C. It is found by multiplying the side length by itself.
500
Find the Surface Area:
90 square inches !
500
For all three expressions, Circle which is greater.
a) 132 or 152
b) 7 x 62 or 63
c) 103 or 302
a) 152
b) 7 x 62
c) 103
500
What kind of polyhedron will this net make?
Square Pyramid
500
Andrew wants to know how much wrapping paper it will take to cover his special edition GTA XI PS5, so he starts to find the volume of the box.
What mistake did Andrew make?
The outside of the box is a surface area measurement, not volume!