Exercise 16.1 A cube has a surface area of \( 1200 \mathrm{~m}^{2} \). Find the area of one face in \( \mathrm{cm}^{2} \).

To find the area of one face of the cube, we start with the surface area. A cube has 6 faces, so to find the area of one face, we can divide the total surface area by 6. Given the surface area \( S = 1200 \, \mathrm{m}^2 \), we calculate: \[ \text{Area of one face} = \frac{S}{6} = \frac{1200 \, \mathrm{m}^2}{6} = 200 \, \mathrm{m}^2 \] Now, to convert square meters to square centimeters, we use the conversion factor \( 1 \, \mathrm{m}^2 = 10,000 \, \mathrm{cm}^2 \): \[ 200 \, \mathrm{m}^2 = 200 \times 10,000 \, \mathrm{cm}^2 = 2,000,000 \, \mathrm{cm}^2 \] So, the area of one face of the cube is \( 2,000,000 \, \mathrm{cm}^2 \).