Exploring Cube Concepts and Calculations

What is the shape of each face of a cube?

• Circle

• Triangle

• Square

• Rectangle

Answer explanation

Each face of a cube is a flat surface that is shaped like a square. This is a defining characteristic of cubes, as they have six equal square faces.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

How many edges does a cube have?

• 6

• 8

• 12

• 16

Answer explanation

A cube has 12 edges. Each of the 6 faces of the cube shares its edges with adjacent faces, resulting in a total of 12 distinct edges.

Tags

CCSS.6.G.A.4

Calculate the volume of a cube with a side length of 4 cm.

• 16 cm³

• 24 cm³

• 64 cm³

• 32 cm³

Answer explanation

The volume of a cube is calculated using the formula V = side³. For a cube with a side length of 4 cm, V = 4 cm × 4 cm × 4 cm = 64 cm³. Therefore, the correct answer is 64 cm³.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Which of the following is a net of a cube?

• A single square

• Six squares connected in a cross shape

• Four squares in a row

• Two squares side by side

Answer explanation

A net of a cube consists of six squares arranged in a way that can be folded to form the cube. The correct choice, 'Six squares connected in a cross shape', allows for this folding, unlike the other options.

Tags

CCSS.6.G.A.4

How many vertices does a cube have?

• 4

• 6

• 8

• 10

Answer explanation

A cube has 8 vertices. Each vertex is a corner where three edges meet, and since a cube has 8 corners, the correct answer is 8.

Tags

CCSS.6.G.A.4

Which shape is not a cube?

• A shape with all sides equal and all angles 90 degrees

• A shape with rectangular faces

• A shape with six square faces

• A shape with 12 edges

Answer explanation

A shape with rectangular faces can include various forms, such as rectangular prisms, which are not cubes. A cube specifically has six square faces, while the other options describe characteristics of a cube.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

If the side length of a cube is doubled, how does the volume change?

• It doubles

• It triples

• It quadruples

• It increases eight times

Answer explanation

The volume of a cube is calculated as V = side^3. If the side length is doubled, the new volume is (2 * side)^3 = 8 * side^3. Thus, the volume increases eight times.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

What is the total surface area of a cube with a side length of 3 cm?

• 18 cm²

• 27 cm²

• 54 cm²

• 36 cm²

Answer explanation

The total surface area of a cube is calculated using the formula 6a², where a is the side length. For a side length of 3 cm, the surface area is 6 * (3 cm)² = 6 * 9 cm² = 54 cm². Thus, the correct answer is 54 cm².

Tags

CCSS.6.G.A.4

Which of the following is a property of a cube?

• It has circular faces

• All edges are of different lengths

• All faces are rectangles

• All faces are congruent squares

Answer explanation

A cube is defined as a three-dimensional shape with six faces, all of which are congruent squares. The other options are incorrect as cubes do not have circular faces, and all edges are of equal length.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Identify the number of faces on a cube.

• 4

• 5

• 6

• 7

Answer explanation

A cube has 6 faces, each of which is a square. This is a fundamental property of cubes, making the correct answer 6.

Tags

CCSS.6.G.A.4