Cubes

We have a cube whose length is $2$ cm and we are asked to find its volume and surface area.

The volume of a cube is equal to length × width × height.

Since the length, width and height of a cube are all equal, in our case the width and height of our given cube will also be $2$ cm. Therefore,

$8=2\times2\times2$

To find the total surface area of a cube, we will first find the surface area of one of its faces and then multiply the result by 6 (remember that cubes are composed of six identical square faces).

The area of each square is
$4=2\times2$

Therefore, the surface area of the cube will be:

$4×6=24\operatorname{cm}$

If you found this article helpful, you may also be interested in the following:

How to calculate the area of an orthohedron - rectangular prism or cube.

How to Calculate the Volume of a Rectangular Prism (Orthohedron)

Orthohedron - rectangular prism

For a wide range of mathematics articles visit Tutorela's website.

Given that:

The length of each side of the given cube is equal to $3$ cm.

Question:

What is the volume of the cube?

Solution:

The volume of a cube (and the volume of a cuboid) is equal to:

Length × Width × Height

Therefore the volume of the cube: $=3^3=27$

Answer:

$27~cm³$

Given that:

Given a cube in which each face has a surface area of $6$ cm.

Assignment:

What is the total surface area of the cube?

Solution:

The total surface area of the cube is the combined area of all of its faces, ie:

Face area

$6\times6=36$

Answer:

$36~cm²$

Given that:

In the given cube, the length of each edge is equal to $3$ cm.

Question:

What is the length of the diagonal of the face?

Solution:

To solve this question we will use the Pythagorean Theorem to find the length of the diagonal of the face:

$A^2+B^2=C^2$

Or, in our case:

$Edge^2+Edge^2=Diagonal^2$

$=3^2+3^2$

$=18$

$\sqrt{18}=3\times\sqrt{2}=diagonal$

Answer:

$3\sqrt{2}$

Given a cube whose edge length is equal to $5$ cm.

Task:

Find the volume of the cube.

Solution:

The volume of the cube is equal to the length of the face of the cube to the power of $3$

We can write it like this:

$5^3=125$

Answer:

$125~cm³$

Given a cube whose volume is equal to $112$ cm³

Question:

How many whole cubes with a volume of $10$ cm³ can fit inside the given cube?

Solution:

We divide the volume of the large cube into $10$ to find out how many cubes of $10$ cm³ fit into the given cube:

$\frac{112}{10}=11\frac{1}{5}$

Since we are only asked about whole cubes, it is possible to enter $11$ cubes into the cube whose volume is $112$ cm³.

Answer:

$11$ cubes.

A cube is a cuboid with six square, equal faces (all the sides are equal).

To find the total surface area of a cube, all we need is the value of one of its sides (since all sides are equal).

Then, we find the surface area of one face by multiplying the side to the power of three.

Lastly, we multiply the surface area of one face by six (since cubes have six equal sides).

Task. Find the total surface area of the following given cube, which has a side length of $7\operatorname{cm}$

Solution:

Let's start by finding the area of just one face:

$Area=7\operatorname{cm}\times7\operatorname{cm}=49\operatorname{cm^2}$

Now, let's multiply the area of one face by six to find the total surface area:

$49\operatorname{cm^2}\times6=294\operatorname{cm^2}$

Answer:

$=294 \operatorname{cm^2}$

The find the volume of a cube, we multiply its three sides.

Remember: since each face is square, all its sides have the same length.

$=$,$\times$

This formula can also be expressed as:

$V=L^3$

since all the sides are equal.

Task. Find the volume of a cube with a side length of$4\operatorname{cm}$

Solution:

Using our formula, we get:

$V=L^3$

$V=\left(4\operatorname{cm}\right)^3=64\operatorname{cm^3}$

Answer

$V=64\operatorname{cm^3}$

Task. Find the volume of a cube with a side length of $8\operatorname{cm}$

Solution:

Again, we will use our formula to find the volume:

$V=L^3$

$V=\left(8\operatorname{cm}\right)^3=512\operatorname{cm^3}$

Answer

$V=512\operatorname{cm^3}$