Cube Volume and Surface Area Practice Problems with Solutions

To solve this problem, we'll follow these steps:

• Step 1: Recall the definition and properties of a cube.
• Step 2: Apply these properties to determine the number of faces.

Now, let's work through each step:
Step 1: A cube is a three-dimensional shape with all edges of equal length and all faces square. It is composed entirely of squares from each face being congruent.
Step 2: By definition, a cube has six faces, each of which is a square. When we visualize a cube, we can think of it as having a front, back, left, right, top, and bottom face.

Therefore, the solution to the problem is that a cube has $6$ faces.

To solve this problem, we'll follow these steps:

• Step 1: Recall the properties of a cube
• Step 2: Identify the number of edges based on these properties

Now, let's work through each step:
Step 1: A cube is a symmetrical three-dimensional shape with equal sides. It has 6 faces, 8 vertices, and 12 edges.
Step 2: Each face of a cube is a square, and the edges are the lines where two faces meet. Since we have established through geometric principles that a cube has 12 edges, this is our answer.

Therefore, the number of edges in a cube is $12$.

To solve this problem, we'll follow these steps:

• Identify the given information: The edge of the cube is 3 cm.
• Apply the formula for the volume of a cube: $V = a^3$.
• Calculate the volume by substituting the given edge length into the formula.

Now, let's work through each step:

Step 1: The edge length $a$ is 3 cm.

Step 2: The formula for the volume of a cube is $V = a^3$. Substituting the given edge length, we have:

$V = 3^3$

Step 3: Calculate $3^3$:

$3 \times 3 \times 3 = 27$

Therefore, the volume of the cube is $27$ cubic centimeters.

Thus, the solution to the problem is $27$ cm$^3$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the properties of a cube.
• Step 2: Count the number of faces and relate to surface area.

Let's go through each step:
Step 1: A cube is a three-dimensional shape with all sides equal in length and each angle a right angle. A cube has 6 faces, each of which is a square.
Step 2: The surface area ($A$) of a cube is calculated as $A = 6s^2$, where $s$ is the length of a side of the cube. The calculation considers contributions from all 6 faces, each being square, hence a cube having 6 faces is integral to the computation of its surface area. The number of faces is 6 and each is involved in computing the surface area through this formula.

Therefore, the statement that all cubes have 6 faces equating to the surface area property is Yes..

To solve this problem, we'll analyze the basic properties of a cube as follows:

• Step 1: Recall that a cube has 6 faces, 12 edges, and 8 vertices.
• Step 2: Crucially, each face of a cube is a square, and a cube has exactly three edges meeting at each vertex.
• Step 3: Count the edges: A cube's geometry dictates that it has 12 edges since each cube has 4 edges per face, shared equally among its 6 square faces.

Now, let's perform a check by thinking through the geometry:

A cube consists of $6$ faces and each face shares its edges with adjacent faces. The twelve unique edges appear as $6 \times 4 \div 2$ edges (since each edge is counted twice, once on each adjoining face).

Thus, it is evident that a cube has exactly 12 edges, not 14.

Therefore, the statement that a cube has 14 edges is False.