Question

A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inch thick:

The figure shows a cylinder of height 16 inches and diameter 6 inches.

What is the approximate inside volume of the pipe? (4 points)

88 cubic inches

49 cubic inches

142 cubic inches

154 cubic inches

Answer 1

To find the approximate inside volume of the cylindrical pipe, we first need to determine the dimensions of the inner cylinder (the hollow part) after accounting for the wall thickness.

1. **Outer Dimensions:**
- Height (h) = 16 inches
- Outer diameter = 6 inches
- Outer radius (R) = Outer diameter / 2 = 6 inches / 2 = 3 inches

2. **Inner Dimensions:**
- The wall thickness is 1.25 inches, so we subtract twice the wall thickness from the outer diameter to find the inner diameter.
- Inner diameter = Outer diameter - 2 × wall thickness = 6 inches - 2 × 1.25 inches = 6 inches - 2.5 inches = 3.5 inches
- Inner radius (r) = Inner diameter / 2 = 3.5 inches / 2 = 1.75 inches

3. **Calculating Inner Volume:**
The volume \( V \) of a cylinder is calculated using the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the inner radius and \( h \) is the height.

4. **Substituting the Values:**
\[
V = \pi (1.75)^2 (16)
\]
\[
V = \pi (3.0625) (16)
\]
\[
V = \pi (48.99999999)
\]
\[
V \approx 3.14159 \times 49 \approx 154.2 \text{ cubic inches}
\]

Therefore, the approximate inside volume of the pipe is **154 cubic inches**.