Question

calculate the volume of solid material of this tube.

call the inner radius (smaller radius) \\(r_{\text{inner}}\\) and the outer radius (bigger radius) \\(r_{\text{outer}}\\).

round your answer to 1 decimal places.

hint: split this problem up into two easier problems, i.e. two cylinders with different radii.

Explanation:

Identify the given dimensions

The problem provides the following dimensions for the tube:

• Inner radius \(r_{\text{inner}} = 5\text{ m}\)
• Outer radius \(r_{\text{outer}} = 5.5\text{ m}\)
• Length (height) of the tube \(h = 12\text{ m}\)

Calculate the outer cylinder volume

Using the Cylinder Volume knowledge point

$$ V_{\text{outer}} = \pi \cdot r_{\text{outer}}^2 \cdot h = \pi \cdot 5.5^2 \cdot 12 = 363\pi\text{ m}^3 $$

Calculate the inner cylinder volume

Using the Cylinder Volume knowledge point

$$ V_{\text{inner}} = \pi \cdot r_{\text{inner}}^2 \cdot h = \pi \cdot 5^2 \cdot 12 = 300\pi\text{ m}^3 $$

Calculate the volume of the solid material

Subtract the inner volume from the outer volume:

$$ V_{\text{solid}} = V_{\text{outer}} - V_{\text{inner}} = 363\pi - 300\pi = 63\pi\text{ m}^3 $$

Round to one decimal place

Evaluate the numerical value:

$$ V_{\text{solid}} = 63 \cdot 3.14159265... \approx 197.9203\text{ m}^3 $$

Rounding to 1 decimal place gives:

$$ V_{\text{solid}} \approx 197.9\text{ m}^3 $$

Answer:

\(197.9\text{ m}^3\)