Find the height of the cylinder whose volume is `1.54m^(3)` and diameter of the base is 140 cm?

Answer

To find the height of the cylinder given its volume and diameter, we can follow these steps:

### Step 1: Convert the diameter to meters
The diameter of the base is given as 140 cm. To convert this to meters, we use the conversion factor \(1 \text{ cm} = 0.01 \text{ m}\).

\[ \text{Diameter in meters} = 140 \text{ cm} \times 0.01 \text{ m/cm} = 1.4 \text{ m} \]

**Hint:** Remember that to convert centimeters to meters, you divide by 100.

### Step 2: Calculate the radius
The radius \(r\) of the cylinder is half of the diameter.

\[ r = \frac{\text{Diameter}}{2} = \frac{1.4 \text{ m}}{2} = 0.7 \text{ m} \]

**Hint:** The radius is always half of the diameter.

### Step 3: Use the volume formula for a cylinder
The formula for the volume \(V\) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height,
- \(\pi\) is a constant approximately equal to \(3.14\) or can be used as \(\frac{22}{7}\).

### Step 4: Substitute the known values into the formula
We know the volume \(V = 1.54 \text{ m}^3\) and the radius \(r = 0.7 \text{ m}\). We will use \(\pi \approx \frac{22}{7}\).

\[ 1.54 = \frac{22}{7} \times (0.7)^2 \times h \]

### Step 5: Calculate \( (0.7)^2 \)
First, calculate \( (0.7)^2 \):

\[ (0.7)^2 = 0.49 \]

### Step 6: Substitute back into the equation
Now substitute \(0.49\) back into the equation:

\[ 1.54 = \frac{22}{7} \times 0.49 \times h \]

### Step 7: Solve for \(h\)
Rearranging the equation to solve for \(h\):

\[ h = \frac{1.54 \times 7}{22 \times 0.49} \]

### Step 8: Calculate the right-hand side
Calculating the numerator and denominator:

1. **Numerator:**
\[ 1.54 \times 7 = 10.78 \]

2. **Denominator:**
\[ 22 \times 0.49 = 10.78 \]

Now substituting these values back into the equation for \(h\):

\[ h = \frac{10.78}{10.78} = 1 \text{ m} \]

### Final Answer
The height of the cylinder is \(1 \text{ meter}\).

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