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:
- \(6 \cdot 3 = 18\)
- \(6 \cdot 3 = 18\)
- \(3 \cdot 3 = 9\)
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.
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