Final answer:
To find the height of the cuboid given its surface area and the area of the base, we can use the formula for the surface area of a cuboid. The height of the cuboid is approximately 0.846 meters.
Step-by-step explanation:
The surface area of a cuboid is given as 148 cm² and we are asked to find its height, given that the area of the base is 30 m² and the perimeter of the base is 22 m. First, we need to address the inconsistency in the units. We will convert the base area to cm² since the surface area is given in cm².
Using the conversion factor (1 m² = 10,000 cm²), we have the base area as 30 m² × 10,000 = 300,000 cm². Since the base is a rectangle and the formula for the perimeter of a rectangle is 2×(length + width), we can write an equation to solve for the dimensions of the base using the given perimeter.
To find the height of the cuboid given its surface area and the area of the base, we can use the formula for the surface area of a cuboid, which is 2*(length*width + length*height + width*height). In this case, we are given that the surface area is 148 cm². We are also given that the area of the base is 30 m² and the perimeter of the base is 22 m.
Let's solve for the height:
2*(length*width + length*height + width*height) = 148
2*(30 + 30*height + height*22) = 148
60 + 60*height + 44*height = 148
104*height = 88
height = 88/104
height ≈ 0.846 m