The inner radius of a pipe is $$ 2 \cdot 1 \mathrm{~cm} $$. How much water can 12 m of this pipe hold ?

Question

UpStudy AI · Accepted Answer

To determine how much water a 12-meter-long pipe can hold, we'll calculate the volume of the cylindrical pipe using the formula for the volume of a cylinder:

$$
\text{Volume} = \pi r^2 h
$$

where:
- $$ r $$ is the inner radius of the pipe
- $$ h $$ is the length of the pipe

**Given:**
- Inner radius $$ r = 2 \times 1 \, \text{cm} = 2 \, \text{cm} $$
- Length $$ h = 12 \, \text{meters} $$

**Steps:**

1. **Convert Units:**
   - Radius from centimeters to meters:
     $$
     r = 2 \, \text{cm} = 0.02 \, \text{meters}
     $$
   - Length is already in meters:
     $$
     h = 12 \, \text{meters}
     $$

2. **Calculate the Volume:**
   $$
   \text{Volume} = \pi r^2 h = \pi (0.02)^2 \times 12
   $$
   $$
   \text{Volume} = \pi \times 0.0004 \times 12 = \pi \times 0.0048 \, \text{m}^3
   $$

3. **Convert Cubic Meters to Liters:**
   - $$ 1 \, \text{m}^3 = 1000 \, \text{liters} $$
   $$
   \text{Volume} = 0.0048 \pi \times 1000 = 4.8\pi \, \text{liters}
   $$
   $$
   \text{Volume} \approx 4.8 \times 3.1416 \approx 15.08 \, \text{liters}
   $$

**Final Answer:**
A 12-meter pipe with a 2 cm inner radius can hold approximately 15 liters of water.
A 12-meter pipe with a 2 cm inner radius can hold approximately 15 liters of water.

The inner radius of a pipe is \( 2 \cdot 1 \mathrm{~cm} \). How much water can 12 m of this pipe hold ?

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