Question
Exercise 16.1 A cube has a surface area of \( 1200 \mathrm{~m}^{2} \). Find the area of one face in \( \mathrm{cm}^{2} \).
Ask by Coleman Tran. in India
Jan 13,2025
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Tutor-Verified Answer
Answer
The area of one face of the cube is 2,000,000 cm².
Solution
To find the area of one face of a cube given its total surface area, follow these steps:
### **Step 1: Understand the Cube's Surface Area**
A cube has **6 equal square faces**. The **total surface area** of the cube is the sum of the areas of all six faces.
### **Step 2: Calculate the Area of One Face in Square Meters**
Given:
- **Total Surface Area** = \( 1200 \, \mathrm{m}^2 \)
Since there are 6 faces:
\[
\text{Area of one face} = \frac{\text{Total Surface Area}}{6} = \frac{1200 \, \mathrm{m}^2}{6} = 200 \, \mathrm{m}^2
\]
### **Step 3: Convert Square Meters to Square Centimeters**
To convert from square meters to square centimeters:
\[
1 \, \mathrm{m} = 100 \, \mathrm{cm} \quad \Rightarrow \quad 1 \, \mathrm{m}^2 = (100 \, \mathrm{cm})^2 = 10,000 \, \mathrm{cm}^2
\]
Therefore:
\[
200 \, \mathrm{m}^2 = 200 \times 10,000 \, \mathrm{cm}^2 = 2,000,000 \, \mathrm{cm}^2
\]
### **Final Answer**
The area of one face of the cube is **2,000,000 cm²**.
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Simplify this solution The Deep Dive
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 \( 2,000,000 \, \mathrm{cm}^2 \).
