A 5.4 cm diameter cylinder has a length of 12.5 cm. What is the cylinder's volume in basic SI units?

검증된 단계별 안내

Step 1: Recall the formula for the volume of a cylinder, which is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height (or length) of the cylinder.

Step 2: Convert the given diameter of the cylinder (5.4 cm) into the radius by dividing it by 2. This gives \( r = \frac{5.4}{2} \) cm.

Step 3: Convert the radius and the length of the cylinder from centimeters to meters, as SI units require measurements in meters. Use the conversion factor \( 1 \, \text{cm} = 0.01 \; \text{m} \). For the radius, \( r \, \text{(in meters)} = r \, \text{(in cm)} \times 0.01 \). Similarly, for the length, \( h \, \text{(in meters)} = h \, \text{(in cm)} \times 0.01 \).

Step 4: Substitute the converted values of \( r \) and \( h \) into the formula \( V = \pi r^2 h \). This involves squaring the radius \( r \), multiplying it by \( \pi \), and then multiplying by the length \( h \).

Step 5: The result will give the volume of the cylinder in cubic meters (\( \text{m}^3 \)), which is the SI unit for volume.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. The radius is half of the diameter, so for a cylinder with a diameter of 5.4 cm, the radius would be 2.7 cm. This formula is essential for determining the amount of space inside the cylinder.

SI Units

The International System of Units (SI) is the standard system of measurement used in science and engineering. In this context, volume is typically expressed in cubic meters (m³). To convert from cubic centimeters (cm³) to cubic meters, one must divide by 1,000,000, as 1 m³ equals 1,000,000 cm³. Understanding SI units is crucial for ensuring consistency in measurements.

Pi (π)

Pi (π) is a mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. It is a critical component in calculations involving circular shapes, such as the cross-section of a cylinder. In the volume formula for a cylinder, π accounts for the circular base, making it essential for accurate volume computation.