Question

a giant model of a magnet is being built for a museum exhibit. What is the total surface area of the prop that will need to be painted to the depth of the magnet 3 feet?

Answer 1

To find the total surface area of a giant model of a magnet that will need to be painted, we first need to determine the shape of the magnet. Commonly, a magnet is often modeled as a rectangular prism (cuboid). For a simple model, let’s assume it would resemble an elongated rectangular shape with a certain width and height.

Let’s assume the dimensions of the magnet are as follows:

- Length (L): 6 feet (for example)
- Width (W): 3 feet
- Depth (D): 3 feet (as given)

Given these dimensions, the surface area (\(SA\)) of a rectangular prism can be calculated with the formula:

\[
SA = 2(LW + LH + WH)
\]

Where:
- \(L\) = length
- \(W\) = width
- \(H\) = height (in our case, it’s the depth, which is 3 feet)

Substituting the values into the formula:

- Length (L) = 6 feet
- Width (W) = 3 feet
- Height (H) = 3 feet

\[
SA = 2(6 \cdot 3 + 6 \cdot 3 + 3 \cdot 3)
\]

Calculating each term:

1. \(6 \cdot 3 = 18\)
2. \(6 \cdot 3 = 18\)
3. \(3 \cdot 3 = 9\)

Adding these together:

\[
18 + 18 + 9 = 45
\]

Now multiply by 2:

\[
SA = 2 \cdot 45 = 90 \text{ square feet}
\]

Thus, the total surface area of the giant model of the magnet that will need to be painted is **90 square feet**.