Question

The area of one face of a cube is given by the expression
3s2+5s. Write a polynomial to represent the total surface area of the cube

Answer 1

To find the total surface area of a cube, we first need to recognize that a cube has 6 faces. The area of one face of the cube is provided by the expression \(3s^2 + 5s\).

To find the total surface area, we multiply the area of one face by the number of faces:

\[
\text{Total Surface Area} = 6 \times \text{Area of one face}
\]

Substituting the expression for the area of one face:

\[
\text{Total Surface Area} = 6 \times (3s^2 + 5s)
\]

Now, we distribute the 6:

\[
\text{Total Surface Area} = 6 \cdot 3s^2 + 6 \cdot 5s
\]

This simplifies to:

\[
\text{Total Surface Area} = 18s^2 + 30s
\]

Thus, the polynomial representing the total surface area of the cube is:

\[
\boxed{18s^2 + 30s}
\]