Given formula for volume (V) = (pi d^2 h)/(4)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Step 1: Identify the given values and formula.
The solid shape is a cylinder.
Given formula for volume ($V$) = $\frac{\pi d^2 h}{4}$
Given diameter ($d$) = $56 \text{ cm}$
Given height ($h$) = $1.2 \text{ m}$
Use $\pi = 3.14$.
Step 2: Ensure consistent units.
The diameter is in centimeters and the height is in meters. Convert the diameter to meters to match the height.
$$d = 56 \text{ cm} = 0.56 \text{ m}$$
Step 3: Substitute the values into the formula.
$$V = \frac{3.14 \times (0.56 \text{ m})^2 \times 1.2 \text{ m}}{4}$$
Step 4: Calculate the square of the diameter.
$$(0.56 \text{ m})^2 = 0.3136 \text{ m}^2$$
Step 5: Perform the multiplication in the numerator.
$$V = \frac{3.14 \times 0.3136 \text{ m}^2 \times 1.2 \text{ m}}{4}$$
$$V = \frac{1.181952 \text{ m}^3}{4}$$
Step 6: Divide to find the volume.
$$V = 0.295488 \text{ m}^3$$
Rounding to a reasonable number of decimal places (e.g., four decimal places):
$$\boxed{0.2955 \text{ m}^3}$$
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