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How to Calculate the Volume of a Cylinder with 11 cm Diameter and 14 cm Height (1 Decimal Place)
Mathematics
Grade 8 of Junior High School
Question Content
Find the volume of this cylinder. Give your answer to 1 decimal place. The cylinder has a diameter of 11 cm and a height of 14 cm.
Correct Answer
1330.0 cm³
Detailed Solution Steps
1
Step 1: Calculate the radius of the cylinder. The diameter is 11 cm, so radius r = 11 ÷ 2 = 5.5 cm.
2
Step 2: Recall the formula for the volume of a cylinder: V = πr²h, where π is approximately 3.1416, r is the radius, and h is the height of the cylinder.
3
Step 3: Substitute the values into the formula: V = π × (5.5)² × 14.
4
Step 4: Calculate (5.5)² first: 5.5 × 5.5 = 30.25.
5
Step 5: Multiply 30.25 by 14: 30.25 × 14 = 423.5.
6
Step 6: Multiply the result by π: 423.5 × 3.1416 ≈ 1330.0 (rounded to 1 decimal place).
Knowledge Points Involved
1
Radius and Diameter Relationship
The radius of a circle is half of its diameter, expressed as r = d/2. This is a basic geometric relationship used to convert between diameter and radius when calculating properties of circular shapes like cylinder bases.
2
Volume of a Cylinder Formula
The formula for the volume of a cylinder is V = πr²h, where V is volume, r is the radius of the circular base, h is the height of the cylinder, and π is a mathematical constant approximately equal to 3.1416. This formula comes from multiplying the area of the circular base (πr²) by the height of the cylinder, which represents stacking the base area along the height to fill the cylinder.
3
Rounding Decimals
Rounding a number to 1 decimal place means adjusting the number so it has only one digit after the decimal point. If the second decimal digit is 5 or greater, the first decimal digit is increased by 1; otherwise, it stays the same. This is used to present numerical results to a specified level of precision as required in the problem.
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