Step 1: Convert units
Since the thickness of the iron sheet is given in centimeters, we should convert the inner radius from meters to centimeters for consistency. \[ \text{Inner radius} = 1 \, \text{m} = 100 \, \text{cm} \] The thickness of the iron sheet is 1 cm, so the outer radius of the tank will be: \[ \text{Outer radius} = 100 \, \text{cm} + 1 \, \text{cm} = 101 \, \text{cm} \]
Step 2: Volume of the Hemispherical Tank (Outer and Inner Volumes)
The volume of a hemisphere is given by the formula: \[ V = \frac{2}{3} \pi r^3 \] - **Inner volume**: Using the inner radius \( r_{\text{inner}} = 100 \, \text{cm} \), we calculate the inner volume of the hemisphere: \[ V_{\text{inner}} = \frac{2}{3} \pi (100)^3 = \frac{2}{3} \pi \times 1000000 \approx 2094395.1 \, \text{cm}^3 \] - **Outer volume**: Using the outer radius \( r_{\text{outer}} = 101 \, \text{cm} \), we calculate the outer volume of the hemisphere: \[ V_{\text{outer}} = \frac{2}{3} \pi (101)^3 = \frac{2}{3} \pi \times 1030301 \approx 2167465.8 \, \text{cm}^3 \]
Step 3: Volume of the Iron Used
The volume of the iron used to make the tank is the difference between the outer volume and the inner volume: \[ V_{\text{iron}} = V_{\text{outer}} - V_{\text{inner}} = 2167465.8 \, \text{cm}^3 - 2094395.1 \, \text{cm}^3 = 73070.7 \, \text{cm}^3 \]
The volume of the iron used to make the tank is approximately \( 73070.7 \, \text{cm}^3 \).