Final answer:
The area of the aluminum piece is 8795.39 cm², calculated by first converting feet to centimeters and then multiplying the length by the width. For the 100-gram hollow cube question, the approximate side length is found to be 1.05 cm.
Step-by-step explanation:
To calculate the area of a piece of aluminum in square centimeters, we must first convert the dimensions from feet to centimeters. Since there are 30.48 centimeters in one foot, the length and width of the aluminum piece in centimeters would be:
- Length: 7.69 ft × 30.48 cm/ft = 234.51 cm
- Width: 1.23 ft × 30.48 cm/ft = 37.49 cm
Now, to find the area, we multiply the length by the width:
Area = Length × Width = 234.51 cm × 37.49 cm ≈ 8795.39 cm²
This is the area of the piece of aluminum in square centimeters.
Regarding the question about a 100-gram hollow cube made from aluminum foil with a surface density of 15 g/cm², we can calculate the side length. Firstly, we know that the surface area (S) of a cube is 6 times the side length squared (6l²), and we can set up the equation:
Mass = Surface Density × Surface Area
100 g = 15 g/cm² × 6l²
To solve for l, we divide both sides by 90 (15*6) g/cm²:
l² = 100 g / (90 g/cm²)
l² = 1.1111... cm²
l = √(1.1111... cm²)
l ≈ 1.05 cm (answer a)