Question

A restaurant built a ramp to make their facility more accessible to people in wheelchairs. They covered the entire surface of the ramp with metal to make it more durable.

How much metal did they use to cover the ramp, including the bottom?

Answer 1

To calculate the amount of metal used to cover the ramp, we need to find the surface area of the ramp. The ramp has a length of 3 meters, a width of 1.5 meters, and a height of 3 meters. The restaurant used 36 square meters of metal to cover the entire surface of the ramp, including the bottom.

Step-by-step explanation:

To calculate the amount of metal used to cover the ramp, we need to find the surface area of the ramp. Since the ramp is a rectangular prism, we can use the formula for surface area: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the ramp.

• Given that the ramp has a length of 3 meters, a width of 1.5 meters, and a height of 3 meters (since the ramp is straight and extends horizontally), we can plug in these values into the formula: SA = 2(3)(1.5) + 2(3)(3) + 2(1.5)(3) = 9 + 18 + 9 = 36 square meters.
• Therefore, the restaurant used 36 square meters of metal to cover the entire surface of the ramp, including the bottom.

Answer 2

The restaurant used an area of (A) square meters of metal to cover the entire surface of the ramp, including the bottom.

Step-by-step explanation:

The amount of metal used to cover the ramp can be calculated by finding the total surface area of the ramp. Assuming the ramp is a rectangular prism, the surface area (A) can be calculated using the formula:

`\[A = 2lw + 2lh + wh\]`

where (l) is the length, (w) is the width, and (h) is the height of the ramp. In this case, the ramp is essentially a flat surface, so (h) (height) would be negligible. Therefore, the formula simplifies to:

`\[A = 2lw\]`

Now, substitute the actual measurements of the ramp into the formula to find the surface area. Once you have the surface area, you can provide the answer to the question, expressing it in square meters.

It's important to note that the use of metal in construction is typically measured in square meters or square feet, depending on the unit system used. This is because metal sheets or panels are often sold in standard sizes with known dimensions, and the area covered is a critical factor in determining the quantity of material required. Additionally, the inclusion of the bottom of the ramp in the calculation ensures a comprehensive measurement, covering all surfaces that were metal-clad.