A rectangular prism is a three-dimensional shape with six rectangular faces. It's like a box, with a length, width, and height. To understand the missing width in our problem, we need to grasp the concept of surface area....
Surface Area of a Rectangular Prism
The surface area of a rectangular prism is the total area of all its six faces. To calculate this, we use the following formula:
Surface Area = 2 * (lw + lh + wh)
where:
- l = length
- w = width
- h = height
Solving the Missing Width
We are given the following information:
- Length (l) = 6 cm
- Height (h) = 4 cm
- Surface Area = 188 square cm
We need to find the missing width (w). Let's substitute these values into the surface area formula and solve for 'w':
188 = 2 * (6w + 6 * 4 + w * 4)
Simplifying the equation:
188 = 2 * (10w + 24)
188 = 20w + 48
140 = 20w
w = 7 cm
Therefore, the missing width of the rectangular prism is 7 cm.
Verification
To confirm our answer, let's plug the calculated width back into the surface area formula:
Surface Area = 2 * (6 * 7 + 6 * 4 + 7 * 4)
Surface Area = 2 * (42 + 24 + 28)
Surface Area = 2 * 94
Surface Area = 188 square cm
This matches the given surface area, confirming that our calculated width of 7 cm is correct.
Additional Insights
Understanding the concept of surface area and its formula is crucial for solving problems related to rectangular prisms. It's important to remember that surface area represents the total area covered by all the faces of the prism. The formula allows us to calculate this area based on the dimensions of the prism.
Practical Applications
The concept of surface area has various practical applications in real-world scenarios. For example:
- **Packaging:** Manufacturers use surface area calculations to determine the amount of material needed for packaging boxes.
- **Construction:** Architects and builders use surface area calculations to estimate the amount of paint or siding needed for a building.
- **Engineering:** Engineers use surface area calculations to determine the heat transfer rate or the amount of force required to move an object through a fluid.
These are just a few examples of how understanding surface area can be beneficial in different fields.